Hi, Jonas,
Sorry to hear about this issue. I'm afraid this is the normal behavior when there are several instances of Teams open. It may be designed to cut down the sync time according to the blog linked below.
https://www.technipages.com/microsoft-teams-dis...
Have you tried using the desktop and web apps (Edge and Chrome) though, instead of opening Teams only in one browser to see if there's any difference?
I also invite you to upvote the existing request for this functionality at the following feedback link:
https://feedbackportal.microsoft.com/feedback/i...
Disclaimer: The first link above is a non-Microsoft website. The page appears to be providing accurate, safe information. Watch out for ads on the site that may advertise products frequently classified as PUP (Potentially Unwanted Products). Thoroughly research any product advertised on the site before you decide to download and install it.
Best regards,