Free way - sign up for a cloudflare account. Use the DNS on cloudflare, they wil put their public ip in front of your www.
Level 2 is install the cloudflare tunnel software on your server and you never need to use the public IP.
Backend access securely? Install Tailscale or headscale.
This should cover most web hosting scenarios. If there's additional ports or services, tools like nginx proxy manager (web based) or others can help. Some people put them on a dedicated VPS as a jump machine.
This way using the Public IP can almost be optional and locked down if needed. This is all before running a firewall on it.
I use them for self-hosting.
If you are using Cloudflare's DNS they can hide your IP on the dns record but it would still have to be locked down but some folks find ways to tighten that up too.
If you're using a bare metal server it can be broken up.
It's fair that it's a 3rd party's castle. At the same time until you know how to run and secure a server, some services are not a bad idea.
Some people run pangolin or nginx proxy manager on a cheap vps if it suits their use case which will securely connect to the server.
We are lucky that many of these ideas have already been discovered and hardened by people before us.
Even when I had bare metal servers connected to the internet, I would put a firewall like pfsense or something in between.
If I run vulnerable software, it will still be vulnerable through a Cloudflare tunnel, right?
Genuinely interested, I'm always scared to expose things to the internet :-).