My efficiency axe mines a drawer too fast for me to be able to reasonably take items out of it. I suggest that if you click on the item sprite of a storage drawer(Or anywhere else on that side of the drawer) you will not break it with the axe in your toolbelt. This is for 1.18.2. Please consider this, it would make the game so much more playable.

Also, if possible, could we make it that double right clicking on a drawer includes items from the deep pockets enchantment?

Adding to this, I think it would be best to implement this as a whitelist/blacklist tag for the client config, That way you can specify which blocks should not summon tools.