I love the concept of the Harbor Freight rechargeable worklight but after three of them that seem to self destruct who can recommend a quality rechargeable worklight that has a strong magnetic, and adjustable.
I use the free HF flashlights. Double up when I need more light. I suppose I could change out the batteries to rechargeables, but I have so many there does not seem to be much point.
Ullman RT2-LTCH Aluminum Rechargeable Rotating Magnetic 24 LED Work Light bought on Amazon I've had for 4 years, lots of use and abuse. Still works great. ( sorry link would not work)
I picked up a pair of these lights last year at Home Depot for something like $14 for 2. Wish I had grabbed a couple of sets at that price as they have proven handy. Still a nice light at $18, but less of an impulse buy item, so I just have the 2. Uses AA batteries which last a long time.
Not sure of the size you were looking for and you did mention rechargeable, in the event you wanted electric I have the Husky 3200 lumen it comes with a multi directional stand.
I use it for detailing my car, it gives out a lot of light and does not get hot.
I have an Astro XL sticklight and love it. It is extremely bright and is rechargeable. I've dropped it a few times but it never faltered. The only small negative is the wimpy rubber flap/cover for the micro-USB charge port. It hasn't broken off (yet) but expect it will sooner than later.
I have made it clear to my wife that I want a Fenix head light for Christmas, the 950 lumens unit.
Not to pricy if it fails, falls in the drink, or get crushed under the lift.... Hyper Tough 600-Lumen Rechargeable Work Light
The light is brighter than any plug in trouble light I ever owned and this is cordless and lasts a long time! Got mine at Walmart for under $20