We have bungee ropes going over the top and down our drawers so when we pick them up (usually by the middle drawer) it all stays together. They then stay like this in our garage until we next go camping, only remove the bungee ropes when we're actually camping or replenishing.
Had plastic storage draws like you wolla, put them in the car and they fell apart, next time glued them and draws fell out the back - stuff everywhere (also tried webbing straps).
Gave up and got a camp fold up cabinet with shelves then transfer stuff to that, used twice and now decided it’s easier to fish around in well labelled big boxes to find what we need (but use a couple of the draws to separate stuff) - also then use boxes as tables.