Let's say that a bag of holding holding valuable items (I don't think it matters what but tell me if it does) was split in two, and
its contents [were] scattered in the Astral Plane.
In order to retrieve these items, can the party use astral projection to gather the items? The spell mentions that the projection has your
game statistics and possessions
but it doesn't mention anything about coming back. The party knows where the items are in the Astral Plane, the only problem is getting them.
If the party can't use astral projection to get the items, how can they get them?
Best Answer
They go on a quest
You can physically travel to the Astral with Plane Shift (or Gate, but Plane Shift is lower level and on more spell lists). If you know exactly where the item is, Plane Shift can get you close (though "close" might still mean days of travel or more, if the DM is mean), and Gate could drop you next to it.
But to be clear, when a Bag of Holding ruptures, the contents are not usually in a known location. "Scattered in the Astral Plane" is roughly equivalent to (if not more hopeless than) "scattered across the Earth". There's no specific place you'll find any given item. In most games, you'd just consider them lost. If they're really important, you Plane Shift/Gate after them (or find a portal to the Astral or whatever) and go looking for them, in the same way people on Earth might quest after the Holy Grail. Feel free to use magic, divine contacts, demonic servants, beat a githyanki to reveal where a collected item was hoarded, whatever, but you're looking for a needle in a very large haystack. Good luck!
Side-note: I ignored Astral Projection in the above, because:
It's arguable whether it provides any means of taking items collected by your astral self back to your real body at all (and if it does, you still have to find a portal to some other plane to do it, and you end up whereever that portal goes, not where you started); ending the spell normally definitely doesn't work (your spirit just snaps back to your body), and finding a portal to another plane has wording that favors an interpretation where you'd only have your original equipment, not whatever your astral self might have collected en route (a generous DM might have the stuff you collected spill through the portal as your spirit transitions through the portal and into the newly appearing original body and possessions).
It's higher level and on fewer spell lists than Plane Shift, and unlike either Gate or Plane Shift, provides no means of appearing near any given place in the Astral.
So even if you knew exactly where your items were, and you have a DM that allows collected items to go through a portal with you, you'd have to travel an arbitrary distance from where you appear to find the items, then travel to find a portal (hopefully to a plane you want to be on), where the same level Gate could have you there and back in moments, and Plane Shift would at least get you close and only require resting to cast it again to return.
If you really want to, Astral Projection is a potential option, it just introduces more complications when you've actually found the items. People tend to think of Astral Projection first, because it has "Astral" right in the name, but the Astral is just another plane, so you can reach it with any technique that allows you to plane hop, and it's usually easier than Astral Projection (which is mostly useful for the "you're pseudo-invulnerable to anything that can't cut a silver cord" and "you can always go back where you started easily" effects, but it's not anything special in terms of planar access).