[4.x]: CP login issues when using replica database

[WHITE-developer]

What happened?

Description

We configured a read replica database, but this causes login issues when there's some lag in syncing with the master db.

At these moments we are unable to login. We don't get a clear error and we are just redirected back to the login page.
In our logs we see the following warning:

web yii\web\User::renewAuthStatus [WARNING] Invalid session auth key attempted for user

Which I can resolve to this line:
https://github.com/craftcms/cms/blob/4.x/src/elements/User.php#L1049

Looks like the record isn't in the replica yet due to the lag. When we disable the replica, it all works fine.
Maybe this query should always be executed on the master db?

Craft CMS version

4.8.5

PHP version

8.2.13

Operating system and version

No response

Database type and version

MySQL 8.0.36 (AWS RDS)

Image driver and version

No response

Installed plugins and versions