iWALK has a range of power banks on sale and all of them are super tiny. Starting from $18, these power banks feature a built-in Lightning connector too.
ChargeUp Pocket 2500 Portable Powerbank Review - Impulse Gamer
Small Portable Charger 4500mAh Ultra-Compact Power Bank Cute Battery Pack Compatible with iPhone 14/14 Pro Max/13/13 Pro Max/12/12 Pro Max/11 Pro/XS Max/XR/X/8/7/6/Plus Airpods and More,Green
Finger Pow charges your phone on the go with small magnetic modules
Anker Nano Power Bank 12W with Built-In Lightning Connector (Black)
POSTUER Small Portable Charger Power Bank 5000mAh Mini Power Bank Ultra Compact Portable Phone Charger Battery Pack Compatible with iPhone (white/pink)
4000mah Power Bank - Heyday™ : Target
ChargeAll 3-in-1 Portable Keychain Power Bank giveaway! - The Gadgeteer
Power Bank and USB Charger
Small Power Bank Portable Charger Battery Pack For iPhone Android Mobile Phone