Symptoms
So, you had one of your AirPors replaced and no matter what you do, you cannot sync it with your older one, so you can't hear sounds from both of them. While you have both of them in the case, the LED on the charging case flashes orange/amber and keeping the button pressed does not turn it into white (doesn't reset). Leaving only one of them in the case, turns the light into stable orange or green though.
Reason
The problem occurs because the two AirPods Pro have different firmware versions, so they cannot communicate each other, and the case and the phone detect them as two different Bluetooth devices. Indeed, if you connect both of them to your iPhone and go to Settings - General - About, you will see two different AirPods Pro connected, with different firmware versions.
Solution
The solution is easy but needs some patience and waiting.
1. Go to Bluetooth, and unpair the AirPod Pro that runs the newest firware version (this should be the older AirPod Pro, not the replacement unit). You can do so, by tapping the circular (i) icon next to it and tapping "Forget this device". Then remove it from the case and store it in a safe place.
2. Now only you new/replacement AirPod should be in the case. Leave it there and just wait. You cannot force immediately a firmware update. Leave overnight the case connected to the charger, with the new/replacement AirPod Pro in it, and your phone 2-3 centimeters from it.
3. Next morning, the AirPod should be updated to the latest firmware version.
Important: For some reason, going to Settings - General - About may still show the old version, even if the AirPod Pro has been updated.
To check if the problem has been solved, unpair the AirPod Pro from the phone (via Settings - Bluetooth),
then put both of the AirPods Pro into the case, close the lid for 30-40 seconds.
Reopen the lid, the light may be again flashing orange but, this time if you keep the button pressed for 15 seconds, it should turn into white normally. You are now ready to re-pair them to your phone and have sound from both of them.
In the unlikely case the light still doesn't turn to white, you have to repeat the whole process and wait a few more hours.
