Looking for the perfect elbow bag

Hello all, as the title suggests, I have no clue what the style of bag I want is called. Pretty much, I’m in search of a birkin that’s not a birkin… the style of bags that you carry on your elbow and is perfect to put in a shopping cart or have in the passenger seat to throw keys and sunglasses and some snacks in. Any price tag, but looking for a good high quality leather that’s quite structured and not too intense branding. The problem is, when I search for small tote I get canvas totes, when I search for small handbag I get crossbody bags, when I search satchels I typically find like mini duffle bags. Here are some bags that are similar to what I’m looking for in terms of structure: Birkin 25 Kelly Prada Saffiano Lux Kate spade satchel Goyard tote mini Marc Jacob’s the tote bag small Polene cyme small I like the Chanel executive cerf but the medium size is my work tote and the small size looks a little odd to me because it’s so short. I know I’m not giving a lot to go off of but figured this would be the place to go. Thanks in advance!:)