How do you handle automatic deployment for websites?

I have a small website with the git code hosted on my own Forgejo instance. I want to give my wife easy access to the code to update texts. I think using Forgejo is an easy enough interface for her to do that.

But how do I ensure that every commit is reflected on the website in a timely manner? I think webhooks are the usual answer. But do I add them to the website itself or do I run a separate service for that? If the latter, can you recommend one?

Or is there a better way? Seems kind of roundabout since the website and Forgejo run on the same hardware.