How to set the ComputeModel property to Serverless on an Azure SQL Database using PowerShell?

Thanks to @holger and @Delliganesh Sevanesan for the help, I was able implement a solution that restores the most recent deleted database (SQL Database), adds some resource tags, and sets the ComputeModel to serverless.

Here's the code:

<# 
Purpose: Restore the most recently deleted Azure Sql Database

Dependencies:
    Az.Sql PowerShell module
#>

# Set variables first
$resourcegroupname = 'myresourcegroup'
$servername = 'myservername'
$databasename = 'mydatabasename'

[hashtable]$tags = @{ 
    application = "testing"
}

try {
    $deleteddatabases = Get-AzSqlDeletedDatabaseBackup -ResourceGroupName $resourcegroupname -ServerName $servername -DatabaseName $databasename
} catch {
    Write-Error "Error getting database backups [Get-AzSqlDeletedDatabaseBackup]: " + $_.Exception.Message
    exit(1)
}

# Get most recent backup in case there are multiple copies
# Assumes index and order in foreach is the same - proven in test
Write-Host "Database backups:"
$index = 0
$MostRecentBackupIndex = 0
$MostRecentBackupDate = (Get-date).AddDays(-2) # initialize variable with date from two days ago
foreach ($db in $deleteddatabases) {
    if ($db.CreationDate -ge $MostRecentBackupDate) {
        $MostRecentBackupIndex = $index
        $MostRecentBackupDate = $db.CreationDate
        Write-Host "Most Recent Database: $($db.DatabaseName) : Created: $($db.CreationDate) : DeleteDate: $($db.DeletionDate)"
    }
    $index++
}

$deleteddatabase = $deleteddatabases[$MostRecentBackupIndex]

Write-Host "----------------------------------------------------------------------------------"
Write-Host "Restoring: $($deleteddatabase.DatabaseName) from: $($deleteddatabase.CreationDate) backup"
Write-Host "----------------------------------------------------------------------------------"

Write-Host "Deleted database info ResourceId: "
Write-Host $deleteddatabase.ResourceId

try {
    Restore-AzSqlDatabase -FromDeletedDatabaseBackup `
        -DeletionDate $deleteddatabase.DeletionDate `
        -ResourceGroupName $resourcegroupname `
        -ServerName $servername `
        -TargetDatabaseName $databasename `
        -ResourceId $deleteddatabase.ResourceID `
        -Edition $deleteddatabase.Edition `
        -Vcore 2 `
        -ComputeGeneration "Gen5" 
} catch {
    Write-Error "Error restoring database [Restore-AzSqlDatabase]: " + $_.Exception.Message
    exit(1)
}

# Wait a few minutes to allow restore to complete before applying the tags
Start-Sleep -Seconds 180

Write-Host "Applying tags to database..."
try {
    $resource = Get-AzResource -ResourceGroupName $resourcegroupname -ResourceType "Microsoft.Sql/servers/databases" -Name "$servername/$databasename"
    New-AzTag -ResourceId $resource.Id -Tag $tags
} catch {
    Write-Error "Error adding tags to database [Get-AzResource, New-AzTag]: " + $_.Exception.Message
    exit(1)
}

Write-Host "Setting ComputeModel to Serverless..."
try {
    # Important - must include -AutoPauseDelayInMinutes 60, -MinVcore, and MaxVcore parameters (thanks holger)
    Set-AzSqlDatabase -ResourceGroupName $resourcegroupname -DatabaseName $databasename -ServerName $servername -ComputeModel Serverless -AutoPauseDelayInMinutes 60 -MinVcore 1 -MaxVcore 2
} catch {
    Write-Error "Error setting serverless mode [Set-AzSqlDatabase]: " + $_.Exception.Message
    exit(1)
}

Write-Host "Database restore complete."