Azure SQL: How can I share replicated db access with specific users?

Question

I have 2 Azure SQL instances :

• db-main which is my main DB, containing both my-db and master databases.
• db-replica which contains a readonly replica my-db@db-main

I have currently a user my-db-admin having db_owner role on my-db database.

I would like to create a specific login (and, if needed, a linked user to this login) with access to only the replicated my-db@db-replica database.

I tried multiple options which are not working so far :

• Option 1

I tried creating a login on db-main + a user on my-db@db-main + granting access to my the database... which is then replicated to my-db@db-replica :

-- To execute on db-main :
use master;
CREATE LOGIN [my-replica-login] WITH PASSWORD='abc';

use my-db;
CREATE USER [my-replica-user] for login [my-replica-login];
EXEC sp_addrolemember 'db_datareader', 'my-replica-user';

I was then able to connect to db-replica with my-replica-user but :

• for some (unknown) reasons it was not having access to my-db@db-replica

Microsoft.Data.SqlClient.SqlException (0x80131904): The server principal "my-replica-user" is not able to access the database "my-db" under the current security context.
Cannot open database "my-db" requested by the login. The login failed.
Login failed for user 'my-replica-user'.

• even if this was the case, I would have preferred to not share credentials between db-main and db-replica

• Option 2

I tried creating my-replica-user only on db-replica ... but given that this DB is readonly, it was not possible.

Do you have any idea on how I may sort this out ?