I'm at a startup, not FAANG, but it's pretty much the same for me, minus the rusty part.

It's fine IMO. Work is about producing value for your employer, so do whatever it takes to do that. Usually it's about meetings, which are pretty much therapy for management.

If you want to be better at code and can't work it into your day job, then you'll have to work on projects outside of work.

Also consider taking it a step farther, and go ahead and initiate some of those meetings or email threads. There's a reason people are making them. They help the team stay in sync and feel better about the project.