A laser that can directly etch the metal will be expensive, but you can do it with a standard engraver using masking. Any of the hobbyist/makerspace units will work - 40 watts (or higher) is sufficient.

Basically, cover your metal cards with some type of masking material, then use the laser to selectively remove the mask exposing the metal beneath. Then you can etch the cards using any of the PCB manufacturing methods, such as this one:

https://hackaday.com/2018/01/25/three-ways-to-etch-snazzy-brass-nameplates/

I have used LiquaMask to good effect for this (not affiliated). It paints on with a consistency of jam, and dries to a thin layer. It's made specifically for laser removal of the mask.

https://community.glowforge.com/t/has-anyone-tried-liquamask/7752

You can also use photo-etch PCB techniques. Depending on the resolution, you can print a mask on a laser printer and transfer using a plastic card sealer. Then etch and remove the resist using standard PCB techniques.