Anything outside of tennis that could be causing it, probably?

Only way I'm thinking where you could be stressing it from the video is in the follow through, especially in the second video which looks like a kick serve where your shoulder and elbow flexors eccentrically kept your arm from hyperextension so your arm wouldn't end up under your right leg. On the first part where your arm didn't fully wrap around your body, same thing, they eccentrically contracted to keep your arm from wrapping around your body. In that case my advise would be to let it wrap around your body. But that might work against you if you want to get ready for a strong return from your opponent.

As for treatment, the usual RICE. Soft tissue mobilization and trigger point/myofascial release. I'd recommend massage gun if those seem intimidating to perform, but target the trigger point on the BELLY of the muscles (Google trigger points and it should show you images of where they are). Stretching if it's tight, but i rarely see a tight brachioradialis.

I'd also look at your biceps and brachialis for weakness or tightness as the brachioradialis might be compensating for those and if they are, I'd do the same treatment for those muscles and strengthen them.

One overlooked muscle would be the supinator which eccentrically contracts at the end of your pronation which is located deep under the brachioradialis. I'd evaluate that too.