My GoPro 7 Black has very good quality, better than any other action camera I've used, and the electronic video stabilization is excellent.
I would assume that the 8 and 9 are slightly better -- at least that's how GoPro has done in the past, each camera is a modest improvement video quality-wise over the previous model. (And I've had several other GoPros over the years, starting with the GoPro HD.)
That said, the battery life is marginal -- about 75 minutes. If you want longer, you'll need some sort of external battery.
I had a Cycliq Fly 6 SE. It was very convenient, and had about 6 hours battery life -- but the video quality was mediocre. Good enough to say what happened in a crash, but ... not great if I wanted to use the footage for something else.
(I say "had", because it stopped working after a rainy ride, out of warranty. It's supposed to be water-resistant, but ... I saw evidence of corrosion on the sd card, I think some water got in there.)
I've tried several other brands over the years, and GoPro has consistently had the best quality (compared to whatever else was available at the same time), but the battery life was always around 75 minutes.
As far as "wiggle and sway" go, I've found that the most important thing there is a solid mount that minimizes vibration. So mount to your frame or seat post if at all possible rather than your handlebars, and keep the mount as short as possible no extensions, for example, as a long mount will wave back and forth as you go down the road.