What issues did you run into with this? I do exactly this in a couple of apps. You can use a `keyup changed delay:${delayMs}ms` event, and you target the area on your page where you want search results.
I also took that approach. The problem wasn't the keyup trigger, moreso trying to make the typeahead suggestions play nicely with radio/toggle filters, plus the results, made things really confusing for me personally. I was taking the approach of ONLY returning HTML from my endpoints and found it hard to mentally model how all the templates were fitting together (probably a skill issue, I am very new to webdev).
Once I abandoned the pure HTML/HTMX approach and just focused on returning a big payload with the search results in JSON and rendering it with vanilla JS, the whole thing became a lot easier.