Cant get the idea out of my head, and did some more research.
The Hero6 by GoPro has an impressively effectively stabiliser, but when I read customer feedback, saying that the item has serious techncial and software problems seems to be a polite understatement. Considering that it is at the top of the price scale, I scratched it off the list.
My current favourite is the Yi 4K+, which sometimes gets labelled "GoPro killer". Its cheaper, but offers also good image quality and stabilisation. It can use GoPro mounts and stuff.
It seems that with a 64 GB SD card, a fast one, i can expect around 70-90 minutes of film, and roughly around the same time drawn out of one battery pack. With two batteries and cards, I can reach into the range of playing time that I want and need, since I would want to focus on the visually more appealing parts of a track - the destination, so to speak - anyway. During a 120km trip, there is maybe 20-30 km of interesting track, so this may work out well. It also depends on choosen image/video format, of course. I assume that something like 2.7K/50, linear format, works well enough for my purposes and allows for some artistic freedom in post processing. Maybe even 1440 or 1080. I do not have nor need a 4K display, 4k does not make sense in TV screens that do not exceed a certain size. But then, there is the thing with the VR mask...
The only question that remains is how well an electric stabiliser will work if attachign the camera to the steering bar of a bike, even when not driving offroad, but plain asphalt. That is the lucky characteristic here in the Münsterland: even small sidetracks, locally called "Pettken", are asphalt, the whole bicycle infrastructure here is quite good. I have seen videos on youtube with Hero6 mounted to the steering bar and the image with EIS on being surpringly calm, i would not have believed that this is possible. I do not wear a helmet and do not want to wear one, I would drown in my own sweat, and it is too German as if I would like to comply with this. In the Netherlands, the people are laughing about German bike riders - and they like the sight, for they can see from far away already that there come the Germans again.
Next I need to check whether I am stuck with Windows for video editing, or if there is software for Linux that does nto make it difficult again or adds difficulty and complexity to the tasks.
Still engaged, the idea is not off the table.