That does sound ideal, but if I could avoid having to buy the battery and charger separately that would be neat.
AA NiMHs are $1.50 to $2. AA NiMH chargers are $10. Mayyyyybe $20 or $30 if you get a fancy one. Are... you SURE that you wanna get more complex than this?
AA NiMHs are damn near disposable in my experience. The trickle-charger ($10 for an 8+ hour slow charger that requires 2 batteries at a time) is fine. If you want a charge within 4 hours or less, that's where $20+ chargers come in. But trickle-charge is fine?
Basically: NiMHs can be left overcharged, as long as they're overcharged slowly. They'll just radiate heat when they reach a state of overcharge, but its actually a safe situation. (maybe reach 120F or 50C temperature during overcharge, but otherwise they're fine). A $10 trickle-charger has no smarts, it just overcharges the batteries you connect. You set a kitchen timer and 20 hours later you take the batteries out, because they're probably overcharged by then.
To answer your question: yes, USB-C AAs exist. But in my experience, the $10 trickle-charger + $2 NiMH is cheaper than buying USB-C AAs. The USB-C charger "inside" the AA also removes room for chemicals (An Energizer or Eneloop AA is 100% chemicals to make as much energy as possible). So you lose on battery life, and the electronics will cause self-discharge (so you'll also have less life).
So you're spending a lot of extra money on worse-specs. IMO not worth it, just stick with the classic NiMH from Eneloop (or reasonable competitors) + standard charger. Buy as much chemicals as you can, lol.
There are USB-C AA chargers btw.
https://www.amazon.com/EBL-Individual-Technology-Rechargeable-Batteries/dp/B077XCKC2G
How long do NiMH batteries hold their charge while not in use?
Modern NiMHs are "LSD", low-self-discharge and have specifications of 1Y to 10Y (!!!) of charge hold. However, older "classic" NiMHs self-discharge within 3 months (!!!!).
The brands I discussed: Eneloop, Energizer, and AmazonBasics, should have over 1Y of charge. If you want an "emergency" battery, I suggest Lithium (not Li-ion, but Energizer Lithium)
These will give you enough charge, and have over 10Y worth of life. But they are NOT rechargable. So they're "emergency use", leave in the car kinda thing. They're also quite expensive ($2+ for non-rechargeable), but their long-life makes them ideal for an emergency use "forget-about-it" battery to leave in a toolbox or something.