Lurker's first post here; I love seeing the projects in this sub. I have patched my partner's hat but now I'm ready to apply some flair. I can remove the white basting thread now that I've stitched around the outside. I haven't embroidered in 40 + years and have blank canvas or blank page paralysis. Would love your ideas.

It's mended, it's visibly mended, it looks great! There's no rule saying you have to add extra decoration :)
I would personally stitch sashiko style over the top, maybe circular like tree rings? It looks like an old school fishing hat, maybe a fish with ripples :)
I think it looks awesome as is.
What kind of stuff do they like?
It looks like it could use a few little fish embroidered on if you really aren't happy with how it looks now, but it's fine as is in my opinion.
Great ideas, thank you!
You could quilt/stitch along some lines of the pattern