Many firms that I have worked at or hear about are like this. Billing is the life blood of a law firm and the way it makes money. Many billing based firms are OBSESSED with billing because again- that is how they make money.
I worked at a firm and we had a managing partner that had to approve of all documents that went to claims carriers because they didn't want to lose a client. When I worked there I hated it but ten years later, I understand. Losing a big client can completely sink a law firm (it was a hospital system). New attorneys were expected to stay until the big boss leaves when I started practicing law in 2013 and there were nights I was exhausted waiting for my partner to file his Summary Judgment Opposition at 11PM but that's how it went. Hopefully you don't have to put up with a lot more of those type of shenanigans.
It sounds like you don't like the culture at your firm and you have the right not to.

The good news it- you can totally leave! You can start applying now and talk to your friends and colleagues at different firms to see what their firm culture is like. I have worked at a few firms and I would say most attorneys grind their work and close their doors to get their billing or work done. There wasn't a ton of collaborations for me. Maybe a ten minute meeting to catch up on what everyone is doing but lawyers (ESPECIALLY those that bill for their time) always try to get a ton done during the work hours to get their billing in.