Slowly but surely Stadia is coming around with more and more stuff, and now that includes a profile page for you and every other player.
This isn't exactly something that is a complete and total surprise. Google has said before that it would add a player profile page to Stadia. It just didn't say when it was planning to implement that change. As it turns out though, that time is now.
Player profiles are live right now and you can check yours out if you want to. That being said Google has only made them accessible from place for the time being.
The Stadia player profile page is only on the web for now
Right now you can only access this content from the website. As noted by 9To5Google, if you go to Stadia.com you can then see your own profile if you click on your avatar in the top right corner.
When viewing your profile, you're not getting a ton of information there. But you do see a breakdown of a few different things. You can view recently played games, and how much time you spent in those games in total is listed along with them.
The profile page also shows how many achievements you have for any particular game. There's a social element that's been baked in too. Google set up the possibility to share your profile. Simply click the share button and the Stadia website automatically creates a sharable link and copies it to your PC clipboard.
From there you can share the profile anywhere you like. You can see the profiles of other players too. And all of the same information is listed on their profiles. What's more, is that at the bottom of each profile page you can view the profiles of each friend. Or the friends of the player that you're currently viewing.
Visible details change with privacy settings
One thing to note is that your privacy settings will more or less dictate what can be shown on the profile page. Likewise, it's the same thing for other people.
If their privacy settings are configured to prevent people from seeing things like achievements, then you won't see achievements on their profile. That's worth keeping in mind as everyone is different, and some players may just prefer to keep those details private from everyone.
So although the feature is live, you won't necessarily be able to see everything on every profile you visit. Friend or not.