While The Orville is mostly a loving homage to Trek, it does call it out on a few things. I think in the pilot episode (or maybe the 2nd), the seat belts in the shuttle save the day (the enemy that boarded it wasn't wearing one, and an "all stop" had real-world results).
The only other call-out I recall is when Captain Mercer says "hail the other ship" and then immediately starts talking. The comms officer interrupts him and says "uh, I haven't opened the channel yet".
I like to imagine there's a whole semester-long unit at Starfleet Academy that deals specifically with footing and movement while the vessel is under attack, because bracing support and soft edges imply conflict is imminent. Which apparently it is every third encounter or so.
When I moved to Japan, and often had to stand on the train with no hand hold, I quickly learned how to lower my center of gravity and balance on two feet against random tilting and turns at high speed.
The university I attended had a tram system between campuses, and there was a certain point when it got to a long, straight stretch of track the car would speed up. There were never enough hand holds for the standing riders, and all the sophomore and above students expected it and just kind of leaned into it while the freshmen would just fall backwards and we'd laugh at them.
Haha. When I first moved to a city, I'd never been on a train before and it was hard. But then I just engaged my surfing muscle memory and suddenly it was very easy. Because I was on a train every day, I always stood hands-free because it felt like good training while I was away from the ocean. Was a fun game.
Why would they even need seat belts? The ship clearly has some form of artificial gravity technology, which they could just use to keep people in their seats despite random accelerations caused by impacts and explosions.
For that matter, why do do they even need seats? The artificial gravity could just keep people in a sitting position.