Admin panel ignores URL path – Nginx

I have deployed WordPress on Kubernetes using Bitnami’s WordPress chart.
I wanted to host WordPress under a specific path, not on root.
To achieve that, I did the following:

• modified wp-config.php file:

define( 'WP_HOME', 'http://example.com/wordpress/' );
define( 'WP_SITEURL', 'http://example.com/wordpress/' );

• created Ingress resource to expose WordPress for public access:

kind: Ingress
apiVersion: networking.k8s.io/v1beta1
metadata:
  name: my-ingress
  namespace: my-namespace
  annotations:
    kubernetes.io/ingress.class: nginx
    nginx.ingress.kubernetes.io/custom-http-errors: '404'
    nginx.ingress.kubernetes.io/rewrite-target: /$2
spec:
  tls:
    - hosts:
        - example.com
      secretName: example-tls
  rules:
    - host: example.com
      http:
        paths:
          - path: /wordpress(/|$)(.*)
            pathType: Prefix
            backend:
              serviceName: wordpress-svc
              servicePort: http

I am able to access example.com/wordpress – I see the default WordPress site:

However, when I go to the Admin panel (I click the WordPress logo at the top), I am taken there, and the URL changes to "example.com/wp-admin/about.php" – normally, it should be "example.com/wordpress/wp-admin/about.php".

Even though the panel displays properly:

When I click on any item on the left, I am taken to the wrong site. For example, clicking on "Users" takes me to "example.com/wp-admin/users.php". I get 404. However, if I modify the URL manually and change it to "example.com/wordpress/wp-admin/users.php", the correct page loads (but the URL in my browser again changes to the wrong one, without "WordPress".

What’s the cause of that?
I don’t see any 30x in the Network tab of DevTools, so I assume that it’s some JavaScript of WordPress that modifies my address bar. How do I stop that?

One more observation – when I click on the default "Hello world" post that WordPress creates by default, it takes me to the correct URL. Only the admin panel seems to not work correctly?