Wordpress as a Tab in MS Teams; login works in Desktop App but not in Browser

[Arnold85]

Hi I want to embed a wordpress(learndash) LMS in Microsoft Teams and want to use OpenID for SSO with the Microsoft/Azure accounts in my Microsoft tenant.
I was able to set up the OpenID add on so that the login does work when I open the Wordpress site directly in the browser. It also works when I add the site in a Tab in Teams on the Desktop App (windows) and on the mobile app (android).
However, when I open Teams as a webapp in a browser it doesn't work as expected. When I click the login button I get forwarded to Microsofts login site where I can login. I then also get redirected to the correct wordpress site from where I clicked the login button. So fas so good, but the site doesn't update to show any content. The login/logout button also still says "login". So I'm stuck in a loop.
Loging in open-id-connect doesn't show any errors.
Do you have any ideas, why it might work everywhere else but in the MS Teams Webapp? Or an advice how I might find the reason?
I uploaded a video to show the behaviour. First directly in Browser (normal), then in Teams as Desktop App (normal), then in Teams as a webapp in browser (error).
https://youtu.be/GY3ikEPzOWo

edit: as you can also see in the video, the user actually gets logged in the teams webapp tab as well (you can see the username in the corresponding field). But the login information seems not to be passed correctly with the redirect.

[Arnold85]

It seems to have something to do with Wordpress being embed in an iFrame (which seems to be problematic for Azure AD SSO in general) and the Samesite attribute in the Cookies.
I'm suprised that I seem to be the only one with this problem here. Maybe still someone has an idea how to solve it?