Wallet Tracker Card, Slim Rechargeable Bluetooth Item Locator, Smart Finder Compatible with Apple Find My for Wallet, Luggage, Passport, IP68 Waterproof (iOS Only) (Carbon Fiber Black)

I've had this one for about 4 months. It seems to work well and is about the width of 2 credit cards. I charged it up when I got it and it still hasn't needed a new charge yet. https://www.amazon.com/dp/B0FS17RCKQ?th=1

I agree with all who've said to just use Find My from a PC or watch. But to address your question, there are several credit card-sized "AirTag-compatible" devices out there for pretty cheap that you could probably tuck inside a phone case. I've got one in my wallet that I got from Amazon that's pretty cool. This one's $14: https://www.amazon.com/dp/B0FS17RCKQ?ref=ppx_yo2ov_dt_b_fed_asin_title&th=1