Prompted by a LightBurn forum discussion, this was completely unexpected:
The color is apparently a side effect of the CO₂ laser vaporizing the plastic, because it emerged during the engraving process.
Polycarb tends to get all melty when cut, so it’s not particularly good for laser machining. Indeed, the engraving produced filaments of (presumably) melted / condensed plastic that I brushed off after taking this picture:
If you could put up with the filaments and the poor cut edges, it might be useful for front panel legends and suchlike.