They don't survive.
They can't fight, so they should AVOID fighting area, in the same way that Carriers Avoid fighting area. Run away, run FAR away (but not so far that your AURA does not affect enemy fleets)

I am fighting the Z area crisis, on Maximum. I CAN defeat a psionic gateway system, however my Support/Aura ships die in the first few days. With all BUFFS and improvements (in fleet+armors, etc) mine currently have 108K Hull, 224K Armor, 103K Shields -- with plenty of regeneration from other effects.

These are the ONLY ships that can carry +15% vs psionic fleet AURA <A> slot components.
If they die in the first few days, there is no value to that <A> slot.

I have 4 varieties of them and qty 5 of each in each of my fleets. So that's 20 ships that die right away per fleet.
Please give them Carrier AI and maybe some 5-10 day invulnerability so they have time to get away from the fighting

Among other things the AURA ship has problems with is, apparently REALLY wanting to be at the front of the FLEET, when a fleet arrives or teleports in, it will be in the FRONT. I found the following in the SHIP's definition within the mod.


Here is the description of that parameter for ships in Stellaris docs.
"formation_priority = <int> Ships with higher formation priority trends to go ahead of the rest of the fleet." - I would think Fifty would be at the vey front.