What would the rarity for a set of bags of holding and similar items like portable hole, that share the same extra dimensional space? It would be similar to how ender chests work in Minecraft, or piggy banks in terraria.

The source item (Bag of Holding/Portable Hole) would work exactly like they normally do, but each source item would have access to the same interior space and work at any range, including across planes.

Very-Rare, maybe Rare depending on the properties of the item itself

With the release of the Unearthed Arcana: Revised Artificer class, Wizards of the Coast introduced the ability for an Artificer to create an item that functions incredibly similarly to how you've specified this object, though weaker:

Many-Handed Pouch

Prerequisite: 4th-level artificer

Item: 2–5 pouches

The infused pouches all share one interdimensional space of the same capacity as a single pouch. Thus, reaching into any of the pouches allows access to the same storage space.

A pouch operates as long as it is within 100 miles of another one of the pouches; the pouch is otherwise empty and won’t accept any contents.

If this infusion ends, the items stored in the shared space move into one of the pouches, determined at random. The rest of the pouches become empty.

—Unearthed Arcana, Revised Artificer, 2019-02-28

Note the prerequisite: a 4th level Artificer. This suggests that as-is, the item described by this feature represents a Common or Uncommon quality item, since the Dungeon Master's Guide specifies the rarity for homebrew items to range around Common at level 3 and Uncommon at level 6.

However, there are a couple of major advantages to the item you've described over the item described in the Unearthed Arcana:

• It has a much larger carrying capacity (500lbs for a Bag of Holding, vs 6lbs for a Pouch, 64ft³ volume vs 1/5ft³


• It can be used at any range, with no limit on being on the same plane (the Many-Handed Pouch has a range limit of 100 miles and cannot be used on different dimensions)


• It can be used by anyone, whereas the Many-Handed Pouch requires at least a friendly Artificer to create the object for them and maintain the Infusion's magic

Because of these advantages, I'd bump up the rarity on this item to at least Rare, and probably Very-Rare. That puts it well above the Bag of Holding's rarity and the [relatively deduced] rarity of this item available to the Artificer class.

Legendary

This is basically a portable and resourceless sending/teleport/plane shift/gate pair of items. The utility of this is massive both in terms of movement and communication.

The primary factors that increase the rating to this level are the planar transfer abilities and the ability to move creatures massive distances. The closest spell that can do this is Gate, which is a 9th level spell and would be a Legendary level scroll that can only be used once. By making this at-will, the item has Legendary status.

Not all Legendary items are combat focused

In fact, there is a Legendary item, the Cubic Gate, that functions very similarly to what this paired/shared item can do:

You can use an action to press one side of the cube to cast the gate spell with it, opening a portal to the plane keyed to that side. Alternatively, if you use an action to press one side twice, you can cast the plane shift spell (save DC 17) with the cube and transport the targets to the plane keyed to that side.

Do note that this Legendary item has limited uses. Although it does allow the actual plane shift spell, which could be considered combat, that isn't it's only function or ability.

There are other Legendary items that are also Utility focused: Sovereign Glue and it's compatriot, Universal Solvent.

Addressing the similarity to Many Handed Pouch

The release of this Unearthed Arcana brings another item into review. However, it's important to note that this is still Unearthed Arcana and has not yet passed balanced review in general. But the item is different enough from the proposed similarity for the following reasons:

1. 
   

   Storage Capacity The UA item has an undefined capacity and only states that they all must have the same. It is unclear if they considered "pouch" to be of equal size as a haversack, bag of holding, or portable hole - but my hunch is that they consider pouch to be much smaller. They could be referencing a standard pouch, but it's unclear.

   
   
   

   
   

   A cloth or leather pouch can hold 1/5 cubic foot/ 6 pounds of gear - or up to 20 sling bullets or 50 blowgun needles, among other things. A compartmentalized pouch for holding spell components is called a component pouch.

   
   

   
   



2. Range limitations. Limiting the range to 100 miles of another pouch and not allowing planar transfer is a major nerf compared to that of the proposed item. This along signifies a major power increase/decrease.

These two factors are significant nerfs to the proposed item and actually support my rating of the proposed item as Legendary.