FWIW, look at the Steam light line of head lamps. 423 battery (never seen a plug in the woods) two brightness's, One will blind you its so strong. I was walking next to my buddy looking for his deer in the dark. He had on his REI special (Petzel) . When I turned mine on his disappeared.
VERY good light, great adjustable , strap and will fit in a small backpack pocket.

FWIW, look at the Steam light line of head lamps. 423 battery (never seen a plug in the woods) two brightness's, One will blind you its so strong. I was walking next to my buddy looking for his deer in the dark. He had on his REI special (Petzel) . When I turned mine on his disappeared.
VERY good light, great adjustable , strap and will fit in a small backpack pocket.

Plenty of plugs in the woods if you are use to being off grid. Non rechargeable speciality batteries are a train wreck in the woods or middle of no where. Go recharge or AA/AAA. My biggest issue with recharging 18650 was the chargers. Felix built in charger is game changer.

Gone down this hole before with stream light and batteries. Great lights up until you no longer have batteries in your center console or pack

Normally I don't associate Harbor Freight and quality. In this case however, I've been pretty pleased with a relatively cheap headlamp I got a few years ago.

Here's their selection page: https://harborfreight.com/search?q=headlamp

The one I've been using is the cheap one for ten bucks. It's not rechargeable. It uses three AAA batteries. In the field it may be easier to just carry extra batteries rather than try to recharge it when it gets too dim. Of course, if you're consistent about recharging that's perhaps not a real problem.

I actually have two. I got one for my hunting buddy to use. They've both worked fine since I got them 3-4 years ago and given no trouble. I'm thinking about upgrading to the 500 lumen model though, just to get more brightness. It is rechargeable.

As I mentioned I usually hesitate to describe items from Harbor Freight as quality but the headlamps I have are working well for me.

Need a spare 18650 charger? I have plenty and would be happy to paint one orange for ya

I got a Fenix HM61R and man that thing is bright when you have it on turbo. It has the magnetic USB charger cable which is nice also. Got 20% off so price wasn't toobad. Great light.

I'm on my 3rd PETZL, been happy with all of them. One is my primary, one is the backup/yardwork light, the other fell out of my pocket and I found it with a truck tire.

This particular model:

https://www.rei.com/product/162477/petzl-tactikka-headlamp?CAWELAID=120217890007141220

These are NOT rechargeable, though, so they may not meet your criteria, OP.

I ran mine for 5 days about hour each day and had a lot left in the tank. Also in sub freezing weather. I was impressed