Hi xCalebDavidx,
May I know what software version your iPad is running? There has actually been an issue with FaceTime calls failing going around on the software version 14.5 and up where the FaceTime would display the "FaceTime Failed" screen or randomly hang up in the middle of a call. FaceTime works on your iPhone and even MacBook if you have one because they use different softwares. Your iPhone uses iOS, MacBooks use MacOS, and iPads use iPadOS. I am experiencing the same issue with my iPad whereas my iPhone X and my MacBook Pro 2019 is just fine. I have tried just about everything down to having my software erased and reinstalled by the people in the store. This is definitely a software issue that has not been addressed yet as people at the store and over the phone have ran 3 diagnostics on my device and nothing was wrong. Similarly, my iPad Air 4 was not working with FaceTime right after I bought it as well. Another piece of information I want to share is that an employee at the apple store I visited told me that another person came in last week with the same issue. They had their device replaced and set up in the store, however the issue still persisted. The issue has not been fixed for that person yet. The employee at Genius Bar told me to call into Apple Support, and ask to speak with a senior advisor, and push this issue to the engineering team since the more people that reports the issue, the faster it will be solved.
Heres a link to another thread of people having the same issue after updating to iPadOS 14.5 and up: https://discussions.apple.com/thread/252737524?login=true&page=1