For sure, you need a public (dynamic) IP for this.

NAT sucks, been there, done that… ugh! And, yeah, nothing can be done short of some sort of proxing that adds latency and unreliability

You need static IP only if you want to host the autoritative DNS server for your domain (spoiler alert: you don’t).

You don’t need to proxy your traffic via VPS (higher latency for no good reason) and the dyndns providers are over priced.

What you need is:

• Buy your domain
• Use a free DNS provider (I used for years the excellent dns.he.net but it is a bit cumbersome. Nowadays I gave up and I now use cloudflare without any proxying, just pure DNS)
• Point your registrar to the dns provider
• use ddclient to update the IP of a domain entry (e.g. server.example.com)
• add as many CNAME as you want that point to that entry (so you can have stuff like Jellyfin.example.com www.example.com Nextcloud.example.com)

That’s all… ddclient will update that single dns entry every time your server restarts (or the IP lease expires and you get a new IP)

The only thing you need to pay here is the domain (you can get free domains but that is another story and tbh I would not recommend, there are cheap domains out of there)