Wrong user info due to cache (is back !)

That's a cache issue indeed. The problem you describe was fixed a couple of years ago in https://git.drupalcode.org/project/welcome_username/-/commit/fa52d823c79...

What Drupal core version are you on?
And what version of this module are you on?

The Drupal core is 9.5.3

The module version is 8.x-1.2

Hi alain_bastard_csf, I cannot reproduce your issue. With core 9.5.3 and module 8.x-1.2
I did install the module and logged in multiple browsers with different accounts.

This test-site has the following cache modules enabled: Internal Page Cache, Internal Dynamic Page Cache.
I also cannot reproduce it with only Internal Page Cache enabled.
And I cannot reproduce it with only Internal Dynamic Page Cache enabled.