Hi ishang baniya •,
Welcome to Microsoft Q&A forum.
As I understand, your PostegrSQL Flexible Server which is stuck in Update State for about 2 hours now which you tried restarting and stopping it via az cli and it didn't work.
Below could be the cases:
While performing upscale or descale, please Ensure no long running transactions happening on the server and Stop or reduce the application intensity workload. Or due to underlying management operations going on could be the reason. I would suggest you to wait for sometime and check again. If the issue is transient, soon you could see server up and running. If not, I would recommend you to raise support case for better investigation of the issue. Let us know if you face any issue in doing so, thanks.