I faced the similar issue and found alternate option.

1, I have created a pwershell script inside the VM "C:\Scripts\winget.ps1" commands inside the script is

winget install mozilla.firefox --source winget

winget install -e --id Google.Chrome.EXE --source winget

2, I have created a task scheduler with below security option.

Click the radio button --> Run whether user is logged out or not

Check this box --> Do not store password

Check this box --> Run with highest privilege

3, Go to Azure VM Run Command Script and run schtasks /run /tn "taskname"

The packages are installed successfully