Odd about the e-mails. That sounds like a bug. As for opening the links in old Teams. You can go to your Default Apps in Windows and modify what opens the ms-teams links etc. there to the preview client if you prefer that and remove from the classic client.

Thanks for sharing the feedback, Rene. Reg. links trying to open classic, it is possible that the specific link you were trying to open is for an app which is not yet supported on new Teams.  Reg. missed chat e-mails, that appears to be a bug. Could you please go ahead and file a support ticket for this?