Like marble, I see them digging the ground tile by tile.
Is that cosmetic or am I running out eventually?

I don't know, but I too would like to know.

No its only cosmetic as they keep going deeper and deeper as needed.

They only go deeper up to a certain point, then it stops and lasts forever. I ran one game until ~500AD just to see what would happen and none of the resources ever depleted.

hI
I think that trees can run out ... but i maybe wrong....

Beakie

Well trees and wild game like boars or deer and wolves for example are re-occuring resources. I.e. they re-appear after a specific amount of time so yes at a certain point of time you can run out of trees in a certain area but if you wait a bit, they will re-appear.

None of the resources run out. Ever. Trees regrow, wild game is bred on breeding grounds (a dedicated tile on the map for each herd), fish keep swimming around, metals are infinite, and quarries never expire. The only limitation you'll run into is only one worker per tile of metals and trees (and wait for them to regrow),

Nothing ever runs out, it may take little time for it to respawn though

Everything is infinite, though trees are still a special case - they regrow if a sawmill "works" them...but if you clean them for space they are vanished forever. So it is the only ressource you are able to destroy in theory, if you aren't careful.

No, the resources are infinite. Nothing is depleted.