THIS IS AN OLD STICKY POST FOR v1.2.1.  I've just placed it here for posterity.

v1.2.1 GOOD NEWS AND BAD NEWS!

Well, basements now link to the parent settlement they're placed in, which is a HUGE improvement!  However, you will be disappointed to learn that if two settlements are linked via a supply chain, the extra items shared will not appear in the basement.  Only the parent's items.  You know how when when you actually LOOK inside a settlement workshop when it's linked, you don't see all the linked items until you open Workshop mode?  It's EXACTLY what is happening here.  The containers don't link when Provisioners are set up, the locations do.

Why?  Well if you're really interested, it breaks down like this:

Provisioners link settlements together by Location (the actual Location record), not by Workshop, or its container.  There is an array stored in memory of which locations are linked.  Then, when the internal native engine workshop mode runs (code which nobody can get to), these locations containers are joined together into memory as a single combined available "Workshop Mode" inventory.
This functionality is not accessible via Papyrus.  So why not do a workaround?  Well here's how that breaks down and why it won't work in any simple way.

In order to make the engine see the provisioner-combined inventory that way, the location of the basement would have to automatically be registered as a new supply chain destination to the parent settlement.  This could be done outside of the code/process of assigning settlers, but doing so sets off a whole chain of other code and script events, including pathing / packages for the provisioner AI to travel, combined settlement data (counts, etc.) and really undermines the entire Workshop foundation.  You would have bugs all over the place, from missing Provisioners, to weird Workshop counts, to who knows what.

It's very clear to me now why Bethesda did not add provisioner linking to Home Plate.  The code is just not set up for it.

In short, it would require many edits to the core Workshop scripts, and a significant overhaul / branching of the Provisioner code, and that's just not something that I'm going to do right now, because it's SO wide reaching, and would effect the entire Workshop function.  Especially with the frequent updates coming from Bethesda.  Nightmare territory.
SO!  You just get a nice middle-ground for now.  Like I said, it's a definite improvement for SURE.  I have a ton of crap in each of my Settlements and it's way better than nothing.  I'll obviously continue to brainstorm ways around it, and something might click.
Cheers.

COMING IN THE NEXT UPDATE

- Fix for being over-encumbered and not being able to enter doors
- Fix for Power Armor marker showing wrong spot on map
- Improved companion sandboxing in the basements
- Map Markers for each basement (misc quest markers, sorry no fast travel yet)