It turns out because on Steam the version is 4.1.1.1524131 and on Stadia 4.1.1.1613044 we cannot play multiplayer with each other.
:-( that is strange - unless they did a patch specifically for Stadia. I imagine there are no patch-notes on Stadia?
To my surprise from time to time they do actually release stadia specific patches and patchnotes. My own theory is that they use the stadia version as a precursor to their console version as it already has gamepad support. Lately, I'm actually wondering of some of the wonkier EA stuff was actually due to the stadia version not being consistently upgraded on all aspects (e.g. control or camera being different from PC version for the moment) but that's pure speculation. Would be interesting to see how divergent both versions actually are. No way to check files on stadia however you can get a download of your saves apparently by google takeout or something. Not sure how useful that would be though
