The astral body you project through the Astral Projection spell "replicates" your possessions while leaving them physically alongside your real body.
Previous questions have argued that Bags of Holding open up to a separate extradimensional space. I interpret that to mean that the extradimensional space is distinct from both the starting plane and the Astral Plane1
Assuming that the 'replicated' Bag of Holding on your Astral form functions2 would it be possible to:
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Have someone on your original plane open the physical Bag of Holding with your body, place an object inside the extradimensional space inside the bag, and close it.
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In the astral plane open the "replicated" bag, and reaching into the same extradimensional space and therefore remove the real item (not just a projection), and close the bag.
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Repeat
My first thought is that this wouldn't work, because the Bag of Holding on your projected form is a replica that might just have the appearance of working, with everything in it being only a replica as well …but it seems by that logic any item projected along with your astral form would also only 'be a replica' and thus not work.
But if this did work, it might be more efficient (but slower) than using a spell like Gate to move objects or carrying them on your person as in other spells.
1I found someone indicating that Bags of Holding in earlier editions actually connected to the Astral but this does not appear to be the case in 5E based on the item description.
2
Admittedly I am not sure that's a safe assumption— apparently this is also different in earlier editions
Best Answer
This is up to the DM.
The spell description simply does not give us a clear idea of the relationship between your real possessions and those possessions you have while under astral projection. Your question here goes well beyond the scope of what the spell description tells us, so you will just have to work it out with your DM. So before you try it, talk to the DM about it so you can come to an agreement away from the table, so you aren’t disappointed if your expectations are subverted by the DM surprising you with a disappointing ruling.