Find My won't detect my replacement AirPods

Have you tried to set the replacement up via this instructions to see if the issues persist?

Set up your replacement AirPods 1, AirPods 2, AirPods 3, AirPods Pro, or a replacement charging case

1. Put both AirPods in your charging case.
2. Connect the case to power, close the lid and wait 20 minutes.
3. Open the lid, then do one of the following:

• • If the status light flashes white, go to step 5.
  • If the status light doesn't flash white, continue to the next step.

1. With the lid open, press and hold the setup button on the back of the case for 15 seconds until the status light flashes amber, then white. If the status light still doesn't flash white, learn what to do. 
2. With the status light flashing white, close the lid of your charging case.
3. Before tapping Connect on the setup animation that appears on screen, go to Settings > Bluetooth, then do the following: 

• • If your AirPods appear in Settings > Bluetooth, tap the More Info button next to your AirPods, tap Forget This Device, then tap again to confirm. Continue to the next step. 
  • If your AirPods don't appear there, continue to the next step.

1. Open the lid, then go to the Home Screen on your iPhone or iPad. 
2. In the setup animation, tap Connect, then tap Done. AirPods are ready for use.