Home Depot doesn’t sell baltic birch plywood, not in store nor online, so whatever you’ve been buying is not baltic birch.
Seconding the PureBond brand for something they carry that laser cuts and engraves easily and consistently. You can get it in 4x8’ sheets, or 10-packs precut to 12x19" for your Glowforge.
There’s a couple different veneers available, and they have 5/32" (“medium”) or 1/4" (“thick”) thicknesses. They’ll cut and engrave at the Proofgrade medium/thick settings.