No not necessarily need gopro style. I would love that fuji but it's a bit expensive for meDo you need a gopro style camera? If not, the Fuji xt-3 video quality far exceeds a go pro.
I don't really know if you have considers everything apart from frame rate. things like poor lighting conditions - zoom range- recording time length - sound- to name but a few. What swung it fore me was having an internal gimbal. Also the hotshoe has contacts fo a mike(apart from the built in stereo mike) so no cables hanging about. What i do like it the quality of a frame taken from a video which is an alternative to just using the stills option.I looked into this having had a panasonic camcorder for many years. it depend of course on what you want to pay but I found the Sony FDR-AX53 to exceed my expetations. It really boils down to if you want videos or stills. However In 4k video mode the camcorder frame rate in the UK is 25fps, the record mode I have at 100Mbps, so don't get confused between the two.

about 500What budget do you have in mind?
A used Panasonic GH4 could be an option.
You should be able to find a nice, lightly used, GoPro 8 black for that, with all the usual accessories, and have a lot of that budget left.about 500