Amazon is kinda filled with fake knockoffs currently.

Any of the modern Petzls or Princeton Tecs or Black Diamonds should fit your bill.

If you can find them on Amazon, Great! But check out the actual sports stores like REI (honestly the headlamps at Walmart work fine) and even better the caver sites I think in the sub description like IMO or OR1 or Elevated.

Eventually caving will most likely lead you into the territory where you're looking at 18650 batteries (like the ones in Vapes) that offer long lasting high power and are rechargeable many times.

The common lights you see in this tier are Zebras (my fave) Nitecores and Fenixes. Any of these lamps is VASTLY superior to any halogen you're most likely using and should open up a world for you.

Good luck and happy caving

Edit:. This is a pretty good lamp we use in our club loaner gear. It's not "rechargeable" but you can use rechargeable AAAs https://www.amazon.com/Black-Diamond-620634-Spot-Headlamp/dp/B06XQFZCPX