Not "insecure" in the sense that they're shoddy with their encryption, no. But being free could possibly mean their incentives are not necessarily aligned with that of the free users.
In security speak, the CIA triad stands for Confidentiality, Integrity, and Availability. I'm not going to unduly impugn Proton VPN's credentials on data confidentiality and data integrity, but availability can be a legit security concern.
For example, if push comes to shove and Proton VPN is hit with a DDoS attack, would free tier users be the first to be disconnected to free up capacity? Alternatively, suppose the price for IP transit shoots through the roof due to weird global economics and ProtonVPN has to throttle the free tier to 10 Mbps. All VPN operators share these possibilities, but however well-meaning Proton VPN and the non-profit behind them are, economic factors can force changes that aren't great for the free users.
Now, the obv solution at such a time would be to then switch to being a paid customer. And that might be fine for lots of customers, if that ever comes to pass. But Murphy's Law makes it a habit that this scenario would play out when users are least able to prepare for it, possibly leading to some amount of unavailability.
So yes, a holistic analysis of failure points is precisely what proper security calls for. Proton VPN free tier may very well be inappropriate. But whether it rises to a serious concern or just warrants an "FYI", that will vary based on individual circumstances.
The latter is not a requirement at all. Plenty of people have publicly-issued TLS certs for domain named services that aren't exposed to the public internet, or aren't using HTTP(s). If using LetsEncrypt, the DNS-01 challenge method would suffice, or can even issue a wildcard certificate for subdomains, so additional certificate issuance is not required.
If after acquiring a domain, said domain can be pointed to one of many free nameservers that provide an API which can be updated from an ACME script for automatic renewal of the LetsEncrypt certificate using DNS-01. dns.he.net is one such example.
OP has been given a variety of options, each of which come with their own tradeoffs. But public access to Jellyfin just to get a public cert is not a necessary tradeoff that OP needs to make.