Okay okay I'll start first
Kokoro - Her headgear (known as ear flaps) is ABSOLUTELY needed as her design, like how a Pokemon or Digimon protag can't be seen without their cap or goggles.
(It was initially based off that lol) She basically is never seen without one and owns multiple designs of it. If she's not wearing one, chances are she's wearing alternatives like a beanie, hooded blanket or cover with a towel. It's just a running joke that you can't see her headgear-less, lol. I didn't come up with any story behind it, but I'd like to think it was a gift from her late mother and she holds a strong attachment to it to wear it all the time.
Sakane - Not as much as Kokoro but both in-story and among TH, she's always pointed out for her huge scarf? She doesn't have many variation of it either, but it's a really notable thing you see in her design mainly for the size, I assume. She doesn't wear it in her casual outfit, but pretty much wear it in mostly her default outfit, This one also have no story-related reasoning other than a simple design trait.
Manami - I wouldn't count this as an accessory but you notice that he is never seen without his green book.
Inside the book, he kept a photo of his friend that already passed away
Yunosuke - Maybe it's not that noticeable but I'm obliged to draw him with his badly-tied necktie in any outfits he have. Apparently he wear one just to look smart. Edit: Another response below mine mentioned about a "smile" being a signature and I think Yunosuke is also counted for that! As stated in his profile, he's always smiling even during serious situation that some actually finds it unsettling that he have no other expressions than smiling despite he can spew out cryptic things when talking lol (And a little fun fact: I always ask people I commission to draw him with a smile because it's the most important thing for his character) Edit again: WAIT....He have more signature design traits than I expected lol but he also must wear his two hairclips no matter what, it's basically the last gift he got from his deceased aunt and he's just never seen without them ever since. The little accessories on his wrists might count as well?
Adding another character, Takuto is always seen covering his head with a hoodie. There's a (spoiler) reason for that, but let's say he doesn't like showing his face much and that's also why I choose to cover his eyes with the long bangs.