I fear the short answer is no but there might be a better way of doing this than using a KeyVault.
I think the solution would be to add the user to the database as an Azure Active Directory user. There are instructions here Add Azure Active Directory User to Azure SQL Database
Go to the SQL server, select Active Directory Admin in the Settings
section
Click Set Admin and choose a user (I'm assuming you if you're setting
all of this up)
Click Save. I forgot this bit first time round.
Now you can sign in to the database with Azure Active Directory -
Password or Azure Active Directory - Universal with MFA
Right click on System Databases/master and create a new query
Run CREATE USER [a.name@example.com] FROM EXTERNAL PROVIDER;
And the user will be added to the database. I'm assuming that you'll still need to set permissions and the like but I think this would give you a simpler solution with more control over what people can do.
Your users might find Azure Data Studio even easier.
https://learn.microsoft.com/en-us/sql/azure-data-studio/download-azure-data-studio?view=sql-server-ver15
This has an Azure section where you can log in with your Azure credentials. Once signed in you can at least discover resources on your Azure subscription and if your account has been granted access as above it's then possible to run queries without any further authentication.