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.