I haven’t deployed Cloudflare but I’ve deployed Tailscale, which has many similarities to the CF tunnel.
Is the tunnel solution appropriate for Jellyfin?
I assume you’re talking about speed/performance here. The overhead added by establishing the connection is mostly just once at the connection phase, and it’s not much. In the case of Tailscale there’s additional wireguard encryption overhead for active connections, but it remains fast enough for high-bandwidth video streams. (I download torrents over wireguard, and they download much faster than realtime.) Cloudflare’s solution is only adding encryption in the form of TLS to their edge. Everything these days uses TLS, you don’t have to sweat that performance-wise.
(You might want to sweat a little over the fact that cloudflare terminates TLS itself, meaning your data is transiting its network without encryption. Depending on your use case that might be okay.)
I suppose it’s OK for vaultwarden as there isnt much data being transfered?
Performance wise, vaultwarden won’t care at all. But please note the above caveat about cloudflare and be sure you really want your vaultwarden TLS terminated by Cloudflare.
Would it be better to run nginx proxy manager for everything or can I run both of the solutions?
There’s no conflict between the two technologies. A reverse proxy like nginx or caddy can run quite happily inside your network, fronting all of your homelab applications; this is how I do it, with caddy. Think of a reverse proxy as just a special website that branches out to every other website. With that model in mind, the tunnel is providing access to the reverse proxy, which is providing access to everything else on its own. This is what I’m doing with tailscale and caddy.
General recs
Consider tailscale? Especially if you’re using vaultwarden from outside your home network. There are ways to set it up like cloudflare, but the usual way is to install tailscale on the devices you are going to use to access your network. Either way it’s fully encrypted in transit through tailscale’s network.