Chrome tanned is grey unless dyed. Veg-tanned is a flashy tan unless died. Vegtan will absorb water readily. Chrome tan won’t. Gets more difficult if additional processes like oiling and/or waxing is done. “Oiled Leather”,for example, is usually chrome tanned then oiled to darken and make more supple. Latigo leather is first chrome tanned then veg tanned (and therefore not good for lasering).
If buying from a vendor, ask them.
To cut down on char, you can wet the vegtan thoroughly, dry off any surface moisture, and laser while still wet. Minimizes char and edge stiffness. If planning to tool, let dry until ready, then tool.
Let dry completely before dying or sewing.
One nice thing about layering leather is that you can pre-drill the stitching holes and get them very even. I make 1/100” (0.01”) diameter circles where I want a stitch hole. Laser, then widen with a sewing awl and get very nice, straight stitches on both pieces to be sewn.