I understand that modern outer layers are more functional. A leather jacket, for example, can be dressed up or down so as to be worn in a variety of situations. It is also better at keeping you warm.
However, I think capes/cloaks are more aesthetically pleasing garments. It also feels good to have the fabric flowing around you as you walk. But what do you think?
Here’s a few that I think are probably more fashionable than a fedora:
Baseball cap, pork pie hat, knit hat (e.g. skull cap, watch cap, beanie), docker cap, scally cap, newsboy hat, ivy cap, ascot, bucket hat.
That’s a great list.
And almost every one of those is likely to work better for OP, work with more outfits, etc, and have less of a stigma than a fedora.
Just a quick note that in the USA, unless there is a sports logo on it, cap = MAGA hat, sorry, dems the rules.
But Breaking Bad hat, now that is a damn fine argument that you made there!? :-P