Apple AirPods Max don't reset to factory settings

Problem.

My Apple AirPods Max don't reset to factory settings.

Steps to reproduce.

I am holding the crown and the noise control button for a while, as described in How to reset your AirPods Max - Apple Support . The headphones flash with amber, but they don't flash with white. I've tried holding the buttons while the headphones are in their case or not, while they are plugged in or not.

I could try unpairing them from Bluetooth, but I believe that in this case they will be removed from my iCloud devices, and someone else might connect to them and claim them.

Why do I need this?

Because my Apple AirPods Max stopped connecting to my iPad and iPhone. No matter what I do, iPad and iPhone don't notice the headphones. The headphones are paired in bluetooth devices (as they should be), but can't get connected even if I press on the "Not Connected" label (previously this worked). Simple restart (when light flashes amber) doesn't help, too.

More background.

The headphones started to malfunction after half a year of me buying them brand new. The problem is with the right ear. Sometimes the buttons stop reacting. Sometimes the sensors stop detecting my head. Sometimes the headphones restart (most common problem), and it can happen 100 times a day (and drives me crazy). Sometimes they shut off, and it is hard to turn them on again. Most commonly these problems happen during movement, which hints to me of some battery problems.

I've tried to repair them at the authorized Apple service, but they said that if the problem goes away by itself, even if I have to put them in their case or plug in to a charger or restart or reset, then it is not covered by the warranty. All problems can't be reproduced consistently, and I was unlucky that they weren't reproduced well at the service center.

Now they are no longer on a warranty, so I can't repair them.