iPhone 11 Pro bluetooth problem

If you have other devices that you used this Earbud with make sure you either temporarily turn of Bluetooth on those devices or move them out of range, they will auto connect and your new phone won't be able to see them. Make sure you have put them in pairing mode and check your manual to see if you need to clear some previous pairings.

My 11 Pro Max doesn't and I know that my friends 11 Pro doesn't because he is currently using it with his Bose BT speaker.

You also checked the manual for your headphones to see what the maximum pairing storage is? Did you try Settings > General > Reset > Reset Network Settings?

I have a similar problem with my new iPhone 11Pro. My Fitbit Inspire worked fine on my iPhone 8 and briefly connected via Bluetooth the first day with my 11Pro - cannot connect again. I also am trying to connect a Garmin device - but Bluetooth will not recognize. Have tried resetting network settings and turning iPhone off and on.