Sped-up version
Short enough to watch multiple times, full-screen,
paying attention to different things each time

Onboard view from Falcon 9’s flight to space and back during smallsat rideshare mission pic.twitter.com/V5PyKxTlWD

— SpaceX (@SpaceX) January 5, 2023

This view is from near the top of Stg-1 looking aft.
Notice how the engine plume gets wider as it gets higher due to the drop in the surrounding air pressure. The plume’s colors also change.
If the cold-gas attitude-control thrusters don’t seem to synch-up with the pitch/yaw motion, remember that the more obvious of the thrusters are high on the body, above the center of gravity.
Also notice that after the re-entry burn, when the atmosphere gets dense enough, the trusters go quiet; and the grid fins take the helm. Gimballing engines do the steering when they’re firing.
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• Previously

Here’s a good, detailed description of what’s goin’ on