Why not just share a screen on discord etc? I feel this would just be toe stepping
Also you can sync YouTube videos, so you get better quality than you would via screen share.
If folks like this, they may also be interested in the neko project: https://github.com/m1k1o/neko
Or even a similar work of my own company: BrowserBox Pro -- where you can share a link to a single browser with multiple people. Co-browsing or co-operative / collaborative browsing is the "term of art" I believe.
I never saw YouTube quality as an issue, but there are watch together extensions for discord.
I think your better off just making an extension.