This ring flash (albeit with 4 more LED's) is available with a rechargeable lithium battery. The unit is called a Godox MF-R76. (MF = Macro Flash). There is a link on this page.

The Godox Ring72 Macro LED Ring Light is a compact lighting solution tailored for macro photography and close-up videography. With 72 LEDs arranged evenly, it offers ample and even illumination to eliminate harsh shadows. Adjustable brightness and color temperature settings provide flexibility to suit various shooting conditions.

Powered by either rechargeable batteries or AC power, it ensures adaptability for on-the-go shooting or studio sessions. The Ring72's compatibility with different camera setups makes it a versatile tool for achieving well-lit and evenly exposed close-up shots.