i have these:
Howard Leight by Honeywell Impact Sport Sound Amplification Electronic Shooting Earmuff, Blackhttps://www.amazon.com/gp/product/B01G8POKMY/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&th=1-- Automatic shut-off feature after four hours saves batteryYou still have to cycle the power switch to turn them on again after shutdown.
i think one thing to consider is, do you really want them to shutoff just at the moment you're about to squeeze the trigger? If your head movement was minimal for a period of time, how long would you want them to remain on? Four hours pretty much meets my outside threshold for inactivity.

The auto-on feature you describe trusts that they will know when you need them on, and when you don't. What if you're still as a mouse to avoid detection, but then need to shoot from the same position? Easy to imagine how the on/off feature would be hit or miss.
I'd recommend having non-electronic hearing protection. Just like a battery-operated gun safe, you don't want to find out the batteries need changing at the wrong time.
Chances are, when you wear hearing protection in the situation you describe, the only thing you'll hear is your heart pounding. if you want to listen for faint sounds, you should have NO hearing protection on. If you want to protect your hearing should you need to shoot, then accept the fact you can't do both.
Personally, it's a matter of priority. i think it's a higher priority for me to identify the person as friend or foe before taking a shot. That likely means turning on a light (lamp, weapon light, flashlight, whatever). Ears are good for knowing someone is there, but eyes are necessary for target identification and acquisition.
It's a dilemma, no doubt. You need to USE your senses up to the point of potentially INJURING your senses.
I'm not sure there's an optimal solution other than to buy an oil filter or solvent trap.
