I have customers contacting me via messenger saying they are trying to buy my work but that due to a 'technical issue' they are unable to check out
If they are asking for email, not real order but a scam.
Probably a scam.
This is most likely a scam. Even if it's true, there's nothing YOU can do. They have to contact etsy directly.
I had this problem too. You can report these messages as spam.
If you are unsure whether or not it's a scam, you can reply "I am unable to assist you with checking out. You will need to contact Etsy for assistance."
But it's probably the beginning of a scam.
As others have said, it does sound like a scam. Next, they will most likely ask for your email to complete the Order. If they do, they don't need it (Mark the Message as spam, just so you don't get dinged for S Seller). When you have a REAL Order, it will appear in your "Orders & Shipping" Page (Left Column in Shop Dashboard). If it isn't there, you have no Order.
I hope this helps you.
OP has 99 sales = not a newbie, and should know how sales look. While it may be the start of a scam, it could also be a temporary glitch that the Buyer is experiencing. Not enough details to know one way or the other.
* @AmandaSelwayStudio really gorgeous art!