It seems that you are using the mobile version of the site. Switch to the desktop version and re-enter mail.google.com in the address bar in the same tab. It should then look the same as the Chrome version.
Strange, I just gave it a try .. i have S22plus (not on beta). Can you try to just replace the link to mail.google.com and see if it changes the layout?
I went into "manage websites" in the "sites and downloads" tab in browser settings (and OMG does that need to be fixed. That is a damned nightmare to find anyting in) and found the gmail and deleted it.
For now, GMail is coming up correctly. We'll see if it stays.
Also, there is no excuse for this to ever happen. It is a bug that Samsung needs to find and quash....it only serves to make DeX less appealing as a desktop/chromebook alternative.