I think I saw someone do an intensive breakdown of this scene where they estimated the density of the logs, calculated their velocity by counting the number of frames it took them to collide with the walker, then calculated the crush resistance of the walker’s frame by measuring how much it deformed in response to the amount of energy the logs put into it.
IIRC, the AT-ST walker has a frame approximately as durable as a family minivan. So… not like terrible… assuming you weren’t taking your walker anywhere more dangerous than soccer practice, but not very impressive for military hardware.
The prevalent weapon in the SW universe are energy weapons. It could be that the AT-ST was armoured against energy weapons and not kinetic weapons. They are also scout vehicles analogous to WWII wheeled scout cars which were lightly armoured.
While not common, kinetic weapons do still exist, and are widely used by outlaws and pirates because of how cheap and easy they are to keep running.
Since I’d wager most of what the empire does by 5BBY is clearing outlaw gathering places, putting down civilian riots, and not fighting against fully equipped rebels (at least not on a scale large enough to matter in terms of designing entirely new units) they would come up against kinetics fairly often. Often enough that they would either need a separate vehicle for patrolling such areas, or the general purpose unit needs more structural integrity.
The empire does like making “good enough” units that can be deployed everywhere, so they really should make the ATST stronger.
They constantly underestimate their opponents, though.