I'm not sure I understand why? If you hosted plex on a vps, you'd still call it self-hosted. I don't see why using (a) fargate or (b) lambda or (c) cf workers changes the calculus here?
But I think changing aws fargate to google or azure alternative isn't a simple as that. It's already vendor locked because the business stake is to high to convert.
Calling it selfhosted but can only selfhost to Cloudflare unless doing heavy modification isn't selfhost.