Install socat or ser2net on HassOS?

That’s not true. Debian 10 + Home Assistant Supervised is the only supported Supervised install on a generic linux OS. However, even if you kept Debian + Home Assistant Supervised, installing other programs is not officially supported. Anyway, not supported doesn’t mean it won’t run anymore, it’s just that the devs won’t bother helping you when you have issues running it this way, the community will still be here to help and there are quite a few people (incl. myself) running “unsupported” installations without any issues.

You can’t install socat or ser2net on HassIO as far as I know.

Take a look here for a good overview of the the different install methods.