I haven't had this refund problem but I have used PayPal hundreds of times through the years both sending money and receiving, and refunds when appropriate without issue. Since all eBay sales are now handled by managted payments through Adyen (instead of PayPal as they once did) I would think the refund should go to whichever payment method you used but PayPal isn't necessarily the method unless you had a balance. If you "use PayPal" there are actually three places the money comes/goes from. If you have a balance in PayPal that is always used first (at least it used to be that way), I haven't held a balance in PayPal since the managed payment system came into play here but imagine it's the same way. If no balance it can come/go from either your bank account or credit card(s). Since in your post you mention both checking your bank balance and credit card maybe you have both set up? PayPal would have requested both primary and secondary sources be set up when opening an account, if you're not sure you can check your wallet in PayPal and it will show you the sources, their order, and expiry dates. It would also show you if maybe a credit card expired, if so, they would try and use your secondary source.
"On PayPal, there's a transaction ID and a date saying it was completed."
You should also be able to see the transaction details that would show actual account it was sent. I know I used to check on the transaction details within PayPal often because I used to go back and forth between using my bank and using credit card so I would look there to double check where something would be processed.
Another thing you mention is your bank doesn't show anything from PayPal. Not sure if it's changed since managed payments but I know in the past statements never said "PayPal", they would have the buyer/seller info and often the names didn't match the eBay user name since PayPal uses email addresses as names.
If you have confirmation of the refunds within PayPal it wouldn't be an eBay issue. As mentioned could be an expired card, or you accidentally changed your primary source when paying.
Lastly I remember getting an email from PayPal some time back than starting a certain date they would be charging a usage fee for inactive accounts (I'm thinking it might have been $20?) if not used for a year. I can't recall the time line but if you were inactive in the account and that date has past is it possible you owed them this fee and your refunds came off of that? If I recall correctly it was taking place in the fall of 2023. I still use my PayPal account several times a year so I wouldn't have received this charge. Any chance it could be that?
I would have thought PayPal customer service would have seen that right off the bat but not sure. I think US is exempt from the inactivity fee but here in Canada I think it applies.
