The description for the Cathedral of the Lost (Nakalim) says that it damages hostile ships by 5%.  I have a Cathedral on a system with a huge influence area, but enemy fleets within that area are staying at 100% health even after several turns.  I am not aware of a ship module that repairs your fleets outside of combat, so it seems like this function of the Cathedral is not working at all.

Hello,

I lack a use case with an ennemy (declared war) fleet near one of my Nakalim System to test the -5% regen ratio but, from what i can see in code and in my own fleets in orbit, it does work

Here is the simulation descriptor for this system improvment

You can see that the regen effects are not directly for this SimulationDescriptor.

They both can be found here

And, id does appear in the simulation

I have a ship in orbit of a system with a Cathedral

And bonus is there

From what i understand it should work provided one fleet of an ennemy (war declared so it does not work with pirates) is in the influence radius of a StarSystem with a built Cathedral

It's a problem with the tag not being applied consistently, not the modifier