Microsoft Teams web app - Add to dock - safari 17 (macOS Sonoma 14.0) - cross-site tracking

Microsoft Teams web app requires "Prevent cross-site tracking" to be turned off in order to run properly in Safari.

Once done, Teams appears to work properly in the Safari web browser.

However, when trying to add that web app to the Dock using Safari's new feature released with Sonoma, the web app seems to be unable to full process the login process: after logging in, the page keeps displaying Microsoft's page asking for which account to use (the account available says "logged in"), and it keeps looping on that page:

So question is: is there a way to also enable cross-site tracking in docked safari web app?

(the "docked app" settings don't seem to have that option, and I'm not sure those docked webapps respect the choices set inside Safari settings)

N.B: I know this is not necessarily Safari's fault (Teams authentication method could be improved too), but I guess I'm not the only who's hoping to have another MS Teams instance/tenent in a dedicated dock icon (instead of having to switch tenent inside the Teams "fat client")