Please review this help article on how to share a video: https://support.ring.com/hc/en-us/articles/115001834066-Downloading-and-Sharing-Your-Ring-Videos
Don't bother submitting any videos or problems here. Ring is just going to point their fingers at Samsung and Samsung will point their fingers at Ring.
Ring has not made a fix to the application to address the problem. As far as whose issue it is, I find it odd that all my other "audio" programs work just fine (video conference calling as one example). The S10 has 2 microphones and I suspect that Ring is not using them correctly. For the S7 and S9 someone suggested to turn off the history feature (sorry if I'm not using the correct name for it). My S7 works ok, but not the S10. The overall app rating for Ring on Android is 2.8 which is not that great (B-/C+). I gave the app a 1 star rating after waiting for nearly 30 days for feedback or acknowledgement of the issue. It's still 1 star for me and I would suggest you do the same. The more people who complain about the issue, it might get noticed and fixed.
There is a work around that sort of works, but is a bit clumsy to use. In live view when you are talking through your phone to the person at the door, hit the microphone mute button immediately after you finish speaking to the person. After they speak, then unmute yourself for your next sentence, then mute yourself again. Keep repeating until you are done. Awkward to use this way, but seems to work.
I had the Note 10+ with screacthing noise. Never was able to get it fixed. No solution from Ring nor Samsumg. Went back to my iPhone and no issues at all.