You certainly can run text editors on Apple Watch.

For example: https://apps.apple.com/us/app/tot-mini/id1644609331

Whether it's a good idea to use a tiny watch screen as your text editor, on the other hand...

That looks like it lets you manipulate some kind of notes object. I wouldn't really call that a text editor.

I don't think there's an app that lets you just edit arbitrary files which can be read by other apps or transferred to/from the watch with something like ssh, just these weird canned things that depend on network services run by Apple and/or the particular developer.