How would you host the video? There’s no chance of doing it cost effectively with the major clouds because they charge 9 cents per gig…. you’d be broke instantly.
So what are some other cost effective ways to do the hosting?
Or it sounds like you might be willing to sacrifice hosting quality and do something like peer to peer storage and serving but that would be a terrible experience for user. Videos would often just not play.
I think you need to raise money for this startup and pay a major cloud provider?
A rough proxy as described is a few hundred lines of Python.
That might get you enough headroom to bootstrap revenue to hosting your own servers colo.
Maybe you can only post 1 second videos, maybe you can only post one video a day, or you only see the most important 10 videos of your friend. With some constraint, there could be alternatives.
Also, probably a dumb idea: can you use cloudflare images for gifs?