iPad 2 activation required and failed (out of nowhere, not activation lock)
The system caches a result that shows the device is activated. You likely have some corruption on the storage and if following the normal activation process fails, support or jailbreak or repair would be next steps.
Doing the activation from a computer lets you get diagnostic logs and may be the best next step if you can’t get it on wireless.
Worst case, try a restore and then consult support online.

https://support.apple.com/en-us/HT201252
https://support.apple.com/

Online support is very good now that the stores have been shuttered for months in most places and staff cross trained to field the online support queues. Support will likely conclude if the device is vintage and for most effectively obsolete and refer to external vendors, though.

https://locate.apple.com/
obtaining support for vintage or obsolete products the iPad 2 is currently “vintage” and soon to be obsolete