I made something crude with python and flask, but it's only to print address labels, always the same settings (paper size and so on)

So i just put a textbox, press the button and it prints there.

When printing generic stuff, you would need to set paper type, paper size, color or BW, if have both sides printed, if printing from a specific tray, then some kind of user authentication (i am lazy and i didn't care about privacy so i used cloudflare access), so the complexity becomes much bigger.

Before making my crude script I searched long time for a free or cheap solution, but I didn't find. If you find, let me know

Just have a web form post a printable file and have the back end use lpr? Are you able to write code for PHP or nodejs?

Sounds like you want savapage https://www.savapage.org/

It by default runs on its own port but that is easy fixable with a reverse proxy.

Gotta say, this question and the process explained threw me for a loop.

You have a network print server where it's advertising an available printer, but instead of the native printer system on a client device, you want to NOT use the CUPS server to print? That's what it's there for. I'm confused on why you have it then.

If your goal is just to have clients print as directly as possible to a printer...you already have that with CUPS running. I guess I'm not getting why submitting via web form is useful in this case.