10 days is pretty long if all the recruiter needed was to get the Hiring Committee approval. I would definitely reach out to follow up. Google does a “blind” committee style final approval to try to eliminate bias. The Hiring manager’s feedback and the interview loop go in front of a committee of a few folks who don’t know the detail of your name, race, sex, etc and who likely aren’t even ion the same team. The theory is this blind committee makes the final hire and at what level decision. Depending on the team, they meat at least once per week if not more.
Don’t worry though, taking this long doesn’t necessarily mean you won’t get an offer, sometime vacations or a backlog of candidates for other roles push your decision out. At 10 days though, you’re fully empowered to check in with the recruiter and ask for a status update. What’s awesome is you’re not even done at that point. If you do get the green light from the Hiring Committee, they’ll tell you and then they’ll send you off to the Compensation committee…. Google is not a fast hiring company…

Yeah this is exactly how I've heard it works from some of my colleagues who work there as well. Definitely check in with your recruiter for an update OP!