How to make it so that it would be impossible to place blocks in the dungeon? Like in Atum 2

Make a block with a completely transparent texture and remember to set it to walkable so you can pass through it, then make the hit box as small a possible so you can interact with stuff still.

Asbjornb way is good idea, though it would need to be also unbreakable, just to ensure.

Another way (imo a bit better, since you can control it more) is putting small, unmovable, transparent entities which would have "add potion to entity in square radius" procedure block - with size determined by you, and custom potion.
And another procedure, this time using global "block is placed" trigger, would be cancelled if this potion is applied to player. This way you can also cancel "block is broken" if you want your dungeon to be unbreakable.