How do working musicians remember so many songs? How can I learn this skill?

I’ve been playing the guitar for a few years and recently shifted my focus to understanding music as a whole and not blindly following TABs. Something that has always mystified me is how working musicians retain so much music and have the ability to play a long list of songs on the spot. How on earth do you start learning this skill?

I’ve been trying to break down things into patterns (like I-IV-V) to find connections between songs. I can tell I’m getting better as a musician, but it’s still hard for me to remember the songs I’ve learned. I feel like I’m picking up new material pretty slowly which is making it even more difficult to remember everything.

Does anyone have any advice or personal experience they’d like to share? Any advice is helpful!

EDIT: Thank you everyone for the feedback! I didn't expect so many people to respond and be so encouraging.