So, does Google already know that I am using the Tor Browser?
Google (and any other website) has the ability to know know, that you are a Tor user because the list of Tor exit relays is public.
Google (and any other website) has the abiltiyability to know, that you are using Tor Browser, because of itsit's browser fingerprint.
Should I do something at my end.
No. Nothing to worry about because of this.
Google's automated abuse prevention systems only "think" it's better to prevent access in this case. (Those abuse prevention systems probably do neither make of use ability 1. or 2.) This is because, too many people are sharing the same Tor exit relay and the abuse prevention systems "think" it is automated access.
Either use Tor Browser's new identity feature and check if that helps or use another search engine.