Not sure what's happening I'm still leaning towards a cable issue even it does read other android devices. I had the same issue with a second hand s8 and the cable that came with it had to use another cable.
Is it still showing up as an error when plugging in.
Have you tried different cables(data) or even a different PC.
Try uninstalling smart switch/kies (reboot PC afterwards). Note: I'm not sure if this removes the usb drivers but it is worth while reinstalling them anyway.
https://www.thecustomdroid.com/download-samsung-usb-driver/
Also to start with use a file explorer to see if phone is recognised ( while in normal/system mode ) as Odin can be a bit touchy in regards to it's com link.
What version of Odin are you using.
Not sure what you mean by phone rebooting into recovery when enabling developer options as generally it shouldn't happen.
Also curious as to what you want to do to your phone.