Remastering is usually done frame by frame, it is very time-consuming, and professional software expensive. There used to be an enhancement program part of Avidemux, but I don't know if It's still going
Avidemux is not an enhancement program, it is a very simple video editor which has an advantage of doing lossless editing of compressed video (with keyframe accuracy). It is very much in active development, like the most of the Linux video software (e.g. Kdenlive, Olive, Flowblade, OpenShot, Shotcut, Vapoursynth, etc.).
For doing good restoration you don't need money, instead you need a lot of knowledge about good video processing techniques. It's a whole science of itself. You can achieve amazing results with VapourSynth and its plugins, all of which are FLOSS, but certainly far from being user-friendly (Python knowledge required, as well as the knowledge on how to compile software from sources). Some simple restoration can be done in Kdenlive, but it's more suitable for editing, and quite excellent at that.
You can also try AI processing with chaiNNer, also completely FLOSS and portable, but a powerful PC with a good video card is necessary for that, and the results may be quite disappointing, so my pick #1 for video processing is still VapourSynth.
Links to check out:
https://www.flathub.org (first and foremost, for the latest versions of everything)
https://www.vapoursynth.com
https://vsdb.top
https://kdenlive.org
https://github.com/jliljebl/flowblade
https://www.openshot.org
https://shotcut.org
https://github.com/chaiNNer-org/chaiNNer