A1427
That is a legacy Apple TV (3rd generation) from 2012. (Unfortunately now officially unsupported for any new software updates or hardware repairs.)
While it can do some AirPlay functionality, there are some services (content providers) that have higher system requirements. Many streaming services that do support AirPlay, now require a receiving device supporting AirPlay 2. For Apple TV boxes, that means model 4th generation or later (A1625 or later).
One example that requires AirPlay 2 for the receiving device, is the streaming service Max. That wouldn’t work with Apple TV A1469 or earlier.
Is it possible my Apple TV is too old to mirror from my devices?
Too old for select services. You should be able to still stream less demanding things, like photos or videos in your iPhone Camera Roll (Photos app).
What type of content were you trying to stream (if you are willing to disclose that)?