False negative on installer screen for DOES THE SERVER EXIST when installing on Azure MySQL
(It's not a recent issue.)
Some details at Stackexchange 1 and Stackexchange 2 but the short version is the DOES THE SERVER EXIST check in the installer is a bit odd - https://github.com/civicrm/civicrm-core/blob/5.16.2/install/index.php#L1038 - it doesn't use the username and password, and then as long as the error is less than code 2000 it says ok that's probably fine. On Azure though the error code is 9002 if you don't provide a properly formatted username and password.
So simple fix is to use the username/password. And it should also use the port for completeness but that's not the problem here.
For reference whether the username/pass is the right combo or not doesn't matter to Azure at this stage, as long as it's the right format it will return the same error code 1045 that the current code receives back from other systems when you pass nulls.
It's not clear if the check even needs to be there when there's similar checks right after - I guess to help narrow down whether the problem is the hostname or something else. But is that really needed.