What happened per your description in your post was a failure in so many ways. The buyer failed to get an accurate pre-approval (apparently) and the lender failed to do their due diligence on the buyer before issuing their "pre-approval" so the buyer could shop for a home. This includes providing all documentation for lender review before the buyer checks out homes for sale. And lastly, your Realtor failed to check the buyers lender before presenting the buyers pre-approval and offer to you. Had you known the buyer had to sell their home prior to closing on your home, you may have not accepted the offer. This info is readily available to your Realtor from the buyers' loan officer prior to any acceptance.

Having said that, how is your market where you are located?

I don't know enough about your specific situation to give advice here, but there are solutions:

1) Put the house back on the market right now;

2) Put in a limited time for your current buyer to sell their home with a "kick out clause" for the current buyer. Ask your agent about this process.

Before you elect to go in option #2 direction, use great caution. How reliable is this lender and the loan officer associated with the mortgage? Many, but not all, of the big box banks have a system in place now where the loan officers are not trained well at all so it is relatively common to have the LO give a "pre-approval" only to have the loan app declined by underwriting a week before closing due to some obvious borrower shortcoming. OR some overlay the big box bank has that isn't present with other mortgage lenders so the borrower doesn't have the issue but the lender has the issue. This can be solved with a different lender.

Just based on your post, I would be very, very cautious with the buyers' lender. The exception would be if this was known up front by the lender and the buyer and the buyers agent failed to disclose. It seems very unlikely that the buyer and the buyer's agent didn't know that their current home had to be sold before they applied for a new VA loan. IME the borrower can only have one VA mortgage at a time.

Have a frank discussion with your agent about your local market.

Is there a way you can purchase your new home without selling your home first? Check with your lender to see what your options are for financing.

Could be they used their VA "entitlement" to purchase their existing home and didn't know, and no one told them, they would have to sell that home to use their VA entitlement to purchase your home. What a mess. Sorry you are going through this.

Does the contract specifically state a VA loan? If not they may just be on the hook for getting a loan.

Did they present you a pre approval letter when they presented you with an offer?

Have your agent call their agent and find out where the screw up happened.