Ghost XL

I used to get heckled about once a month and looked into this. The cycliq was way out of my price range so I got a ghost drift xl on sale for a bit over a hundred and got a helmet mount. The visual quality isn't the greatest and I've heard that image stabilisation without being on a helmet isn't great, but it works and it's got great battery life. I look like a dork but ironically have not gotten heckled since.

I use a Ghost XL mounted under my Garmin. Easily get 10 hours of battery life and continuous recording. Seen them around $99 on Amazon.

I tried several cams including Drift Ghost XL, Drift Ghost 4K, and a cheap Akaso 4K action camera. None of them could reliably show a license plate at a reasonable distance. "4K" is almost meaningless I've found... just because it'll output that many pixels doesn't mean they have worthwhile information. I ended up with a DJI Osmo Action 5 Pro which produces really nice footage and you can make out license plates from a good distance. It also wasn't crazy expensive compared to some of the cycling specific options like the cycliq. I mount mine in between my handlebars in front which works decently well, though I would really like something for the rear in addition. Getting an 8K 360 cam would probably solve this though my concern was that the ability to see plates wouldn't be as good.

Drift Ghost XL is a little over your budget but it is much sleeker than a GoPro and works well as a dashcam (overwrites old footage, decent battery life). Cheaper than that and you're into random no-name Chinese stuff that may or may not be OK.

Dji osmo action 5 pro forward facing. On hyperlapse recording. Varia 715 rear facing. I tried a ghost xl, but needed to return it, as it was unsuitable for me.

Helmet cam > handlebar cam I use a Drift Ghost XL. It's an older model, just 1080p so it soesn't always get a good read on fast-moving plates - no big deal, just call out plates in NATO phonetic for the audio. But it's light, sturdy, the battery lasts a week of commuting, and I don't need a huge SD card. I've heard some iffy things about the higher-res Ghost models. I'd probably try one if my XL dies but I feel no burning desire to upgrade. I briefly tried a Innovv H5. I do left-side mount (I'd take out a top mount in a week) and it was just too much leverage on a lightweight bike helmet, but it was a really nice camera and I'd highly recommend it.

Your one would be the ghost series by drift innovations. Best standalone for this use case. Works like a dash cam, mounts well and good battery life.

Drift Ghost of AliExpress will be about $100. 6 hour battery at 1080p, dashcam mode, and an app that allows you to download videos over the air at the side of the road. A bit clunky to mount to a helmet, but I have a seatpost mounted rear facing one, and one on the GoPro adapter under my out-front Garmin mount. It's been enough to get a few positive outcomes from UK police.