Couple of misconceptions. You're protected if the airline goes bankrupt if you pay using PayPal and use a credit card. Paypal provides protection even if you use an EFT (e-check) or debit card. The charge will show up as PayPal*Merchant Name. When you use PayPal it'll let you select any card or bank account you have on file, or any funds on deposits with them. You can even add a card at that point.

As for OP it sounds like AA.com hiccuped and didn't issue a reservation. (If they can't find your PNR that is the case) If AA can indeed find the reservation, but isn't showing it as paid then you have another issue that is easier to fix. If however they don't show a reservation at all then they'll have to start from scratch. If the reservation is there they can contact PayPal to get it fixed. If no reservation at all then they'll need to redo it like it was a brand new reservation. As if the first charge posts to your account depends on if AA actually communicates to PayPal that it completed the transaction. That is normally done right away. However since no reservation appears to exist it may not have. If it did it'll post at some point and need to be refunded, or it'll never post and the hold will drop. If it does post and they later charge you again they'll refund it.

For those saying not to use, I use it all the time. All my recent Qatar airway purchases have been via PayPal. Of course QR issues tickets instantly so you know right away if there's an issue. As noted PayPal provides better protection then a CC even.

BTW for reference I've had several recent AA.com purchases with credit card provided directly that didn't ticket. Seems to be an aa.com issue.