I just use a card case in my medium flap. I put folded bills in one back pocket and extra cards in the other back pocket. For coins, I end up dumping them in my small makeup pouch (along with my makeup and other essentials) & periodically clean out the coins.
Initially, I used my compact Prada wallet. It’s similar to the LV Zoe? (Very small bi-fold).All my items fit, but just barely. But I just got so sick of the squishing that I became a card case convert.
My mom uses a no-name wallet that is long & flat& super thin. It has card slots on the side and a center zip for cash & coins. (She always has a ton of cash & will never fold bills). There is a similar wallet online from Dior. (I haven’t examined it yet but it looks intriguing). I think Ysl has one like that, too. (But it has fewer sections and I’m not sure if it is small enough. Again, check them out in person). My mom’s is so usable because it’s not to tall, either.
Good luck & happy hunting!