Look for "diode laser cnc". If you search for "laser cutter" or "engraver" the results get mixed in with all kinds of larger machines.

The world of home laser apparati is kinda wild.

These are typically called "laser engraver" when you search for them but they advertise cutting features and cut well. 99% of them have a 5w laser diode, there are 10w and 20w models which just combine several 5w diodes somehow. Each one seems to double the price.

Searching for Comgrow, Creality Falcon, Atomstack, or Sculpfun laser engraver will get you pretty far.

Edit: I should add the more dishonest chinese sellers will advertise "20w or 40w laser engraver" and what they mean is the entire machine consumes 40w with a 5w optical output. Dont be fooled.

Yes, laser cutter/engraver.