I'd recommend a purse or messenger bag, that's what I use when I wear a skirt (that doesn't have pockets). Also could just wear a hoodie and put it in the front pocket(s), that also works.
Backpacks are mostly good if you want to carry bigger or much more stuff. For everyday stuff though, not really necessary since it'll just be my Phone, my Wallet, a bottle of Advil, and maybe my Steam Deck (in case I want to kill time Gaming while I wait).
Also you can put enamel pins on a messenger bag, and depending on the material it works just as well.