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Would cloudinary be able to handle user uploaded content?

yes, there are 2 options (as I recall):
upload direct from the client, which uses a preset you define in the cloudinary console
upload to server then from there to cloudinary.
There pretends to be a third option where you send the video to storage and cloudinary grab it automatically, but that's really very expensive

yes cloudinary allows you to upload from the client using a preset you define in the cloudinary console. Cloudinary is most useful if you want to do multiple transformations on the same content: it can do size and quality and it can even create moving thumbnails

you can create folders on the fly by defining the route: {user_id}/{content_id}

or you can have one bucket and tag the media with the user_id

wonder if cloudflare can do it with their R2 solution

I love cloudflare  https://www.cloudflare.com/products/cloudflare-stream/