I'm not very knowledgeable in the area and was hoping someone could help me figure this out. There's no power located anywhere near my closets and the camping headlamps we currently use are not cutting it.

I'd like to add some LED strips for closet lighting for a couple of small closets in my apartment. The Dewalt drill batteries that I currently use are their "20V MAX" (20V, 1.3Ah, 26Wh) so I'd like to use those or something compatible (https://www.dewalt.com/en-us/products/accessories/batteries-and-chargers?Facet1=System%3b%3b20V-s-MAX-ax--s-%3b%3b20V-s-MAX-ax--s-|&pageNum=1).

I'm thinking of running the lights around the inside perimeter of the closet door (approximately 16' total) using a "daylight" LED strip like this one (https://www.amazon.com/dp/B078JP8X99). It's (300 LEDs, 12V DC, 60W).

I'd like to wire the LEDs to some sort of cradle so that I can pop the battery out and replace it with a fresh one and wire in a reed switch to turn on the lights when the door is opened. For the cradle, I'm hoping that I can buy or make one, but if necessary I could buy some of these work lights (https://www.amazon.com/dp/B0052MILZM) and chop off the part where the battery attaches.

Is this possible? How do I avoid blowing something up? How would I calculate the battery life? Are there other types of battery that would be more appropriate, like a power bank for charging cellphones and whatnot?

Bonus: I'd like to add in an ESP8266 chip like a wemos D1 mini using ESPHome (https://esphome.io/) to connect the whole thing to my Home Assistant, but that's really not necessary.

I'd appreciate any help, thanks.