Shit shit this really feels like old mecha anime Where they used human brain to control the mecha
I think this one specifically is referencing specifically Evangelion.
Date-A-Live is has quite a few shoutouts/references to Evangelion
Ratotskr's logo is basically the NERV logo.
The whole city going underground and evacuate into shelter thing is basically from Evangelion.
AT Fields.. I mean Territories and only being able to defeat the Angels... I mean Spirits with said means (there are some differences since it's not a copypaste duh).
I guess some usage of the Kaballah (not as much of a link here) and thus some Biblical angel names.
A company making special equipment that can use said AT... I mean Territories... with a hidden conspiracy to cause a supernatural disaster and wipe out humanity (though I guess this one is closer to the Rebuilds with like WILLE vs NERV and shit so uh yeah, but it's also probably a reference)
These are the ones I remember off the top of my head.