I have an SSDT tSQLt project which deploys fine to both SQL Express/localdb and Azure

(Though I don't in practice find deploying to Azure and running tSQLt unit tests there adds any value compared to just having the CI pipeline run them against localdb - but your milage may vary - tSQLt tests are primarily about testing your code is written correctly and this should be pretty agnostic to what platform you run it on)

There are differences between Azure SQL and on premise that might need testing (e.g. default isolation level of RC vs RCSI might cause different behaviour under conditions of concurrency) but tSQLt unit tests aren't for testing that.

The configuration I use as the debug database is localdb 2019 on which the following has been run

USE [master]

EXEC sp_configure 'show advanced options', 1; RECONFIGURE;
EXEC sp_configure 'clr strict security', 0; RECONFIGURE;
EXEC sp_configure 'clr enabled', 1; RECONFIGURE;

The "Target Platform" is "Azure SQL Database" and that deploys without complaint to SQL Server 2019 local db.

It does mean that I need to restrict myself to syntax supported in both editions but this is rarely an issue (If I get an overwhelming urge to use LEAST and GREATEST then I can always use SQL Server 2022 local db instead)

Occasionally I have a need to use syntax only supported in Azure but I tend to find this is only post deploy scripts and I can add a IF @@VERSION LIKE '%Azure%' check to stop it running in localdb (and hide any incompatible syntax like CREATE USER ... FROM EXTERNAL PROVIDER in EXEC blocks).