Reading the wiki page for Foraging it says the chopping down trees will give Forage experience and I'm wondering if the EXP gain is gated to just the axe or whether you can throw a bunch of mega bombs down and create a small ecological disaster while still gaining the EXP for having "cut down" (in a manner of speaking) the trees.
If I remember correctly, bombing things does not give you EXP. Either for foraging or for mining if you do it in the mines. It's just a quick shortcut.