Should I paint layered cuts before or after assembly?

I've done a few of these stacked mandala pieces and the workflow that worked best for me is basially what you're describing, with one extra step. Prime and paint every layer flat first, assemble, then go back over the whole assembled piece with one light spray coat at the end. That final pass evens out the seams, covers any scuffs from handling, and blends the touch-up spots so you can't tell where they are. Don't try to make the pre-assembly paint perfect, just get it 90% there and let the last coat do the cleanup. For the primer itself, spray is defintely the way to go on 3mm ply. Brush primer on mandala cutouts is misery, it pools in every corner and you'll be picking globs out of the fine stuff with a toothpick. Two light coats with a light scuff of fine sandpaper between them, and the same with your color coats. Multiple thin coats beats one heavy one every time, especally in the detailed areas where thick paint will shrink back from the edges and leave you with fuzzy lines. One thing to think about before you paint: wood glue doesn't stick well to painted surfaces. Either leave the glue zones raw by masking them off before priming, or plan to scrape a little paint off the glue lines. I've had decent luck using CA glue on these instead of regular wood glue since it bonds to paint a lot better and you barely need any, so less squeeze-out to clean up. Whatever glue you use, wipe the squeeze-out imediately, dried glue on painted edges is a pain to remove without taking the color with it. As for skipping primer on an interior piece, I wouldn't. Birch ply soaks up paint unevenly and you end up needing way more topcoats to get solid coverage, and without primer the paint can chip at the cut edges where the veneer layers are exposed. Primer is cheap, just don't skip it. Also, do your final spray coat with the piece laid flat, not hanging on the wall. Gravity plus wet paint plus tiny cutouts equals drips exactly where you don't want them.

Another thing that saved me on my last stacked piece: I drilled tiny registration holes thru the backing layer and used toothpicks trimmed down as pins to hold everything in place while the glue set. Meant I barely touched the painted faces during assembly, just the edges. Also learned the hard way to paint the backs of the layers too, even though nobody sees them. Bare ply on the back will pull moisture at a diffrent rate than the painted front and I ended up with a slight bow on one piece within a month. Took ten extra minutes per layer, worth it.

Funny reading this, back in the day we did the same layered look with a scrollsaw and it took forever, so enjoy your laser doing it in an afternoon. One trick I picked up from those years: seal the raw ply edges with a wiped-on coat of shellac before you prime. The laser cut edges on birch ply are fuzzy and drink paint like a sponge, and they're exactly where your fine detail lives. Quick pass with a rag, dries in minutes, sands back smooth. I still keep a can of the stuff around for jobs like this, old habits die hard. Curious what colors you're going with, dark on light or the reverse?

Update: went with the plan from the first two replies. Painted everything flat, used the toothpick pin trick for assembly wich was way less stressful than I expected. Tried the shellac wipe on the ply edges like the scrollsaw guy said and it does make the cut edges feel way smoother under primer. One thing I'm stuck on though, do you sand the shellac coat lightly before priming or just prime right over it?