Unless I’m misunderstanding the reliability and utility of rechargeable flashlights

You are. We nearly always recommend flashlights here that use rechargeable batteries. We often recommend flashlights that can charge the battery inside the flashlight. Most of us do not recommend lights with non-removable batteries though as all batteries degrade over time and having spare batteries can be very useful.

The go-to entry-level light around here is the Wurkkos FC11. I recommend the linked version with the 519A LED because the light it produces has a more pleasant color (less likely to look green) than the others, but all of them are above average and have excellent color rendering, which helps you see details.

The FC11 uses a standard 18650 Li-ion rechargeable battery, which is included. There is a USB-C port on the light for charging the battery internally and in 2023 you probably already have a USB charge port of some sort in your car. The brightness is fully adjustable, and the battery is roughly equal to ten alkaline AAs in capacity.

You can buy spare batteries like this one and a separate charger like this one if you want to be sure you won't run out. That charger also acts as a USB powerbank, using the batteries to power other devices if you want.

I drop the flashlight because I’m too concentrated on holding the food

Given that, maybe consider a headlamp.