[2021] Launcher Play Button Not Working Intermittently

The game version does not change the launcher version. You should be on 2021.7.2 now, is that what you see?  

Then I have no real explanation for this happening to you. Do you have a lot of mods subscribed perhaps?  

2021.8 just came out, did that change anything?

If not, can you reduce the number of mods you are subscribed to?  

Are you both on launcher 2021.8.2 ?  

Then I can't really explain how you can have this problem, especially with no mods installed.

I see you have CSL which uses the same launcher - does it happen there?