It is difficult to do an inlay in solid wood. The density and grain structure messes with getting a clean and even pocket depth.
The MDF core of Proofgrade plywood is very good for an inlay. You can get an even depth of pocket.
There are different power level, speeds and LPIs for achieving the effect you want. You might be tempted to just burninate it all at once. That can leave a buildup of soot at the edges of the engrave. I often do less aggressive engraves and do multiple passes. That way the burn gets blown away rather than accumulating around the edge of the inlay.
I also clean the edges of the inlay with a dental pick to get the corners of depth sharp.