I have no idea what mod that is
@Plasmaboo but the storage in a storage thing has always been possible, just causes issues and potentially world corruption from too much NBT in one spot. From what I remember there is also a set limit to the amount of times you can nest tags with NBT so that would be an issue too.
For my most recent cool discovery, Gany's End + Tinkers' Construct + AE2 is an awesome combination. Although it's really Gany's End that's the good one, it includes a new material with a special property after all that is insanely useful for mining. If you make a tool from endium, or with TiC any tool part is endium on creation, it will grant the tool the ability to bind itself to an inventory and all blocks mined or drops from mobs killed will teleport straight into that inventory instead of actually dropping. AE2 comes into it because the interface has the nifty property of counting as an inventory, so all three mods combined allow you to create TiC hammers that teleport all blocks mined straight into your ME system, it doesn't work across dimensions but it's still very useful as you can rebind with incredible ease.
Nesting limit is 512 (seems to be a limit of the implementation and thus of the specification, rather than an intrinsic limit). You're unlikely to hit that unless you hit a bug that leads to infinite recursion or some other form of excessive recursion, or if you intentionally use a mod like this to reach the limit. I can't think of a legitimate reason to nest storage more than 500 deep, and you'll probably run out of CPU/RAM/GPU first.
The more likely limit you'll hit first is not intrinsic to NBT itself, but to the Anvil/Region format. The region header contains the location and size of each chunk in the file - measured in sectors of 4 kiB. The chunk size is a single byte, meaning that each chunk can be up to 255 sectors large (just under 1 MiB). Chunk data is compressed, but this limit could still be theoretically exceeded if a crapload of stuff (i.e. NBT data) were to be crammed in a single chunk. If the chunk data, after compression, exceeds 255 sectors, it cannot be correctly saved and thus world corruption will occur (the world will probably still be recoverable, but best case you lose the chunk, and worst case you lose the region). I can't really think of a conceivable way to hit this limit in Vanilla besides possibly entity spam (which would probably freeze the computer of anyone loading the world before the limit is reached), or doing some really silly shit like cramming items/mobs with really long random strings as names in the chunk. Mods which encourage storing lots of information in a small space (such as AE2, but excessive items moving in pipes could also do it) may also risk hitting the limit. But again, if the compression algorithm is good at compressing entity spam, it would take more effort to exceed the limit.
I might try scanning my current world with a Python program to see what the largest chunk I have is.
EDIT: Biggest chunk in my current world is 19 sectors (all others are smaller than 10). Don't know where it is other than that is it in the Overworld (well, I know the coordinates, but don't remember what is there).
EDIT2: It's in my base, and it's the chunk that contains all the ME storage in my main base (so most of my items), which makes sense.