The worst I've seen is that Google serves an ancient version of their homepage to Firefox mobile for "reasons". With an extension to spoof useragent to Chrome, you get the regular page and it works fine
Used to be the case with Google Maps as well, Chrome user agent would get you served with a faster version.
The worst I've seen though isn't by Google themselves. It's user-agent whitelisting on other web sites, that think it's okay to prevent users from using the browser they want because they couldn't spend time testing in the other browsers. Sometimes they even exclude Chromium. For that reason I have an user agent spoofing extension on each of my browsers.
IMO, Google put a new stage on embrace extend extinguish I call "neglect". Make everything open source and nice, then continue to update G specific functionality by simply not maintaining good support for anything else.
Google probably has the best engineers and greatest minds since IBM in the 60's, possibly ever. But great engineers are attracted to shiny objects, and if all of those are Google objects there's suddenly no reason to use anything else