The only thing that happens when I click the button is this lighted panel
https://imgur.com/a/ub4tjMY

Please provide a logfile.

Here are my latest general log files if that's what you want as I wouldn't know what kind of log file you otherwise want.
Reason that I'm sending multiple is that I don't remember restarting my game

latest.log
2022-08-12-1.log.gz
2022-08-11-1.log.gz
2022-08-11-2.log.gz
2022-08-11-3.log.gz

i have the same issue
latest.log

I have the same problem.

Turns out the GUI is there, just invisible.
I randomly clicked around and my browser opened with the login prompt.
Login then worked fine.

I join the problem. She only appears with Optifine.

Thanks for the hint with Optifine - Looks like Optifine has a Bug and doesnt support one of Forges features correctly.
A Workaround has been added to v4.0.7 which should make it possible to use ReAuth with Optifine