Screen Time blocks Google websites because YouTube is restricted
Your problem is that Google, as part of its single sign-on (SSO) process, also logs you into YouTube. For most of the Google applications, it can set cookies that are valid on *.google.com, but for YouTube, it redirects you to https://accounts.youtube.com/accounts/SetSID with a sign-on token; you can see this URL briefly flash up when you log in.
It's this redirect that's tripping up your filter. As described in other answers, you can restrict your filter to www.youtube.com, or you might be able to explicitly whitelist accounts.youtube.com.