The full set of Android processes running as root on my Pixel 2 is https://pastebin.com/sTtQVz3m - which of these is from Play Services?
I think that in most cases the system services that are in a position to interfere with the keyboard in any way are provided by the phone manufacturer rather than Google - obviously if you're running gBoard then Google has control over that, but I'm not aware of any way that Google fundamentally has control over the other frameworks that the keyboard interacts with (but, again, I don't work on Android - I'd love a more definitive answer on this)