I cannot get wired headphones to work through lightening adapter with iPhone 13 Pro Max

Is this the Apple lightning adapter? Or one from a third-party? My experience has been this adapter, especially, the third-party ones, can go bad more quickly than one might expect.

Have you tried testing the headphones on another device that has a regular headset jack? If the headphones work on another device, the problem is either the adapter or the phone. If they don't work on a device with a regular headphone jack, you need new headphones.

Have you tried testing the adapter and headphones on another iPhone? If they don't work, the issue is probably your phone. The first thing I would do is try cleaning the lightning port. Even if the phone is charging, there might still be enough lint in there to prevent the headphones from working. Under a strong light, with a magnifier if you have one, use a non-conductive tool such as a toothpick to carefully remove any pocket lint or other debris that might have gotten jammed in there. It's amazing how much can get wedged in the back.

I take it you've already adjusted the volume, you can check this guide

If your headphones don't work with your iPhone or iPad – Apple Support