What governs columns rendered in Azure CLI determined for output table

Since the Azure client command az ad is using Microsoft Graph API, since mid 2022 ^ref, you can dig into Microsoft Graph API documentation to have some of the information you need.

This page is, I believe, the corresponding API endpoint used by the Azure client call.

Digging further that route, we can see that there is an chapter named Applications, under Microsoft Graph REST API v1.0 endpoint reference.

And that chapter teach us that there is an application resource type, which is most likely JSON you are getting as a return from your client call.

The same page lists the properties of that specific resource type.

Here is a reproduction of those properties at the time of writing this answer:

Property	Type	Description
addIns	addIn collection	Defines custom behavior that a consuming service can use to call an app in specific contexts. For example, applications that can render file streams may set the addIns property for its "FileHandler" functionality. This will let services like Office 365 call the application in the context of a document the user is working on.
api	apiApplication	Specifies settings for an application that implements a web API.
appId	String	The unique identifier for the application that is assigned to an application by Azure AD. Not nullable. Read-only. Supports $filter (eq).
applicationTemplateId	String	Unique identifier of the applicationTemplate. Supports $filter (eq, not, ne).
appRoles	appRole collection	The collection of roles defined for the application. With app role assignments, these roles can be assigned to users, groups, or service principals associated with other applications. Not nullable.
certification	certification	Specifies the certification status of the application.
createdDateTime	DateTimeOffset	The date and time the application was registered. The DateTimeOffset type represents date and time information using ISO 8601 format and is always in UTC time. For example, midnight UTC on Jan 1, 2014 is 2014-01-01T00:00:00Z. Read-only. Supports $filter (eq, ne, not, ge, le, in, and eq on null values) and $orderBy.
deletedDateTime	DateTimeOffset	The date and time the application was deleted. The DateTimeOffset type represents date and time information using ISO 8601 format and is always in UTC time. For example, midnight UTC on Jan 1, 2014 is 2014-01-01T00:00:00Z. Read-only.
description	String	Free text field to provide a description of the application object to end users. The maximum allowed size is 1024 characters. Supports $filter (eq, ne, not, ge, le, startsWith) and $search.
disabledByMicrosoftStatus	String	Specifies whether Microsoft has disabled the registered application. Possible values are: null (default value), NotDisabled, and DisabledDueToViolationOfServicesAgreement (reasons may include suspicious, abusive, or malicious activity, or a violation of the Microsoft Services Agreement). Supports $filter (eq, ne, not).
displayName	String	The display name for the application. Supports $filter (eq, ne, not, ge, le, in, startsWith, and eq on null values), $search, and $orderBy.
groupMembershipClaims	String	Configures the groups claim issued in a user or OAuth 2.0 access token that the application expects. To set this attribute, use one of the following valid string values: None, SecurityGroup (for security groups and Azure AD roles), All (this gets all of the security groups, distribution groups, and Azure AD directory roles that the signed-in user is a member of).
id	String	Unique identifier for the application object. This property is referred to as Object ID in the Azure portal. Inherited from directoryObject. Key. Not nullable. Read-only. Supports $filter (eq, ne, not, in).
identifierUris	String collection	Also known as App ID URI, this value is set when an application is used as a resource app. The identifierUris acts as the prefix for the scopes you’ll reference in your API’s code, and it must be globally unique. You can use the default value provided, which is in the form api://<application-client-id>, or specify a more readable URI like https://contoso.com/api. For more information on valid identifierUris patterns and best practices, see Azure AD application registration security best practices. Not nullable. Supports $filter (eq, ne, ge, le, startsWith).
info	informationalUrl	Basic profile information of the application such as app’s marketing, support, terms of service and privacy statement URLs. The terms of service and privacy statement are surfaced to users through the user consent experience. For more info, see How to: Add Terms of service and privacy statement for registered Azure AD apps. Supports $filter (eq, ne, not, ge, le, and eq on null values).
isDeviceOnlyAuthSupported	Boolean	Specifies whether this application supports device authentication without a user. The default is false.
isFallbackPublicClient	Boolean	Specifies the fallback application type as public client, such as an installed application running on a mobile device. The default value is false which means the fallback application type is confidential client such as a web app. There are certain scenarios where Azure AD cannot determine the client application type. For example, the ROPC flow where it is configured without specifying a redirect URI. In those cases Azure AD interprets the application type based on the value of this property.
keyCredentials	keyCredential collection	The collection of key credentials associated with the application. Not nullable. Supports $filter (eq, not, ge, le).
logo	Stream	The main logo for the application. Not nullable.
notes	String	Notes relevant for the management of the application.
oauth2RequiredPostResponse	Boolean	Specifies whether, as part of OAuth 2.0 token requests, Azure AD allows POST requests, as opposed to GET requests. The default is false, which specifies that only GET requests are allowed.
optionalClaims	optionalClaims	Application developers can configure optional claims in their Azure AD applications to specify the claims that are sent to their application by the Microsoft security token service. For more information, see How to: Provide optional claims to your app.
parentalControlSettings	parentalControlSettings	Specifies parental control settings for an application.
passwordCredentials	passwordCredential collection	The collection of password credentials associated with the application. Not nullable.
publicClient	publicClientApplication	Specifies settings for installed clients such as desktop or mobile devices.
publisherDomain	String	The verified publisher domain for the application. Read-only. For more information, see How to: Configure an application’s publisher domain. Supports $filter (eq, ne, ge, le, startsWith).
requestSignatureVerification	requestSignatureVerification	Specifies whether this application requires Azure AD to verify the signed authentication requests.
requiredResourceAccess	requiredResourceAccess collection	Specifies the resources that the application needs to access. This property also specifies the set of delegated permissions and application roles that it needs for each of those resources. This configuration of access to the required resources drives the consent experience. No more than 50 resource services (APIs) can be configured. Beginning mid-October 2021, the total number of required permissions must not exceed 400. For more information, see Limits on requested permissions per app. Not nullable. Supports $filter (eq, not, ge, le).
samlMetadataUrl	String	The URL where the service exposes SAML metadata for federation. This property is valid only for single-tenant applications. Nullable.
serviceManagementReference	String	References application or service contact information from a Service or Asset Management database. Nullable.
signInAudience	String	Specifies the Microsoft accounts that are supported for the current application. The possible values are: AzureADMyOrg, AzureADMultipleOrgs, AzureADandPersonalMicrosoftAccount (default), and PersonalMicrosoftAccount. See more in the table. The value of this object also limits the number of permissions an app can request. For more information, see Limits on requested permissions per app. The value for this property has implications on other app object properties. As a result, if you change this property, you may need to change other properties first. For more information, see Validation differences for signInAudience.Supports $filter (eq, ne, not).
spa	spaApplication	Specifies settings for a single-page application, including sign out URLs and redirect URIs for authorization codes and access tokens.
tags	String collection	Custom strings that can be used to categorize and identify the application. Not nullable. Strings added here will also appear in the tags property of any associated service principals.Supports $filter (eq, not, ge, le, startsWith) and $search.
tokenEncryptionKeyId	String	Specifies the keyId of a public key from the keyCredentials collection. When configured, Azure AD encrypts all the tokens it emits by using the key this property points to. The application code that receives the encrypted token must use the matching private key to decrypt the token before it can be used for the signed-in user.
verifiedPublisher	verifiedPublisher	Specifies the verified publisher of the application. For more information about how publisher verification helps support application security, trustworthiness, and compliance, see Publisher verification.
web	webApplication	Specifies settings for a web application.

^{Source: https://learn.microsoft.com/en-us/graph/api/resources/application#properties}