I've figured out, that the Medieval Overhaul mod is causing issues to the logic of Deep Storage.
Every cell will be limited to a single stack of time (no matter the size, even if 10 or 999 units).
The rustic medieval storage containers (from their mod) are using the regular "3 items per cell" stack logic of RimWorld itself (vanilla logic "ShelfBase"), which is working as usual and expected.

The developer of that mod also stated that they have removed the mod dependency of LWM Deep Storage (just as an announcement, nothing else being said, but was probably also causing lots of issues with their themed-stacking buildings?).

Leaving all medieval based mods and anything else I use in but removing Medieval Overhaul from the mod loading order will result in Deep Storage working as intended (multiple predefined stacks per cell).

The load order of Deep Storage <> Medieval Overhaul has no effect in Deep Storage working as intentional.

There are no log errors whatsoever!