“this would be better without the laser” — I’m surprised we don’t see more inlay/marquetry projects here, as that’s one of the few areas where a laser cutter really shines. Another is complex fretwork.
“style of laser engraved products” — One of the curses is ubiquitous flatness. I’m learning to always incorporate a third dimension. When I did these ornaments, the flat version looked very laser-cut and boring (not to mention easily replaceable by a printed picture). By simply making it more layered, it became very elegant and not at all reminiscent of laser-cutting.
Look for ways to combine crafts. Lots of examples here. This clock was mostly laser-cut, but the traditional woodworking in the edge trim saved it from looking like a laser project. Or remember the artwork made from fabric.
Get inspiration from AI image generators. Once in a while they produce something that can be tweaked into a usable design, like these Halloween decorations.
Sometimes the AIs go crazy and give you something you think is impossible … then you start wondering if you can do it. I asked for a simple flat pinecone laser-cut Christmas ornament, and I got this instead, which I’m going to attempt… I have some ideas…