I am looking for help transferring all data (almost 2TB) from an old AirPort Time Machine
Time Machine is software on your Mac that is used to back up the data on the Mac to another hard drive. You probably meant to say that you have an AirPort Time Capsule, which is hardware.....a Wi-Fi router with a built in hard drive.
When I try and do back ups to the time machine from my MacBook, I get a "drive is failing" message.
Unfortunately, the hard drive on the AirPort Time Capsule must be operating correctly if you want to transfer a copy of the data on the Time Capsule over to another hard drive.
In other words, if you cannot back up your Mac to the AirPort Time Capsule at this time, it is going to be extremely difficult....and expensive....to physically pull the hard drive from the Time Capsule and then have a data restoration specialist try to rescue the data on the Time Capsule hard drive.
As a test.....Do you have a spare blank USB hard drive that you could connect directly to the USB port on the AirPort Time Capsule to see if it is possible to "archive" or copy the contents on the Time Capsule to the USB drive?

Worst case......if you cannot get at the data on the failed Time Capsule hard drive.......you will have to start all over again with a new complete Time Machine backup of your Mac to the QNAP drive and move forward from there.