The best course of action is to submit a
bug report on this.

If it's already been reported, it's another instance of the issue, with up-to-date saves and reproduction steps. If it hasn't been reported already, well then we learned something new today, and it's gonna be a
good day.
Thanks Mr.Freake. I made a thread, albeit poorly in comparison to
@Liggi a couple of weeks ago, and I'm just trying to piggy back onto and continue this thread -which to me is about more than a bug report and just ties into the general problems of Federations. I will submit one about the federation presidency though, if its not confirmed as being submitted.
Other issues though for Federations -
1. Federation fleets/ships being deleted by an AI and rebuilding the federation ships. (As though its costing some upkeep)
2. Federation ships splitting up and not "doom stacking" as if they were a traditional fleet. It should never or rarely happen. A 600 ship fleet should only split up into no more than 3 fleets, if it even should at all. It's meant to be a galaxy 'deterrent' and a show of power and should be used as such in larger fleet battles.
From a playthrough perspective this is particularly really important because a federation is meant to change the odds, to make a fight possible, to even up end them. It also gives you something to "worry about" when a galaxy has become polarised e.g. "where is their navy, it can decimate my space if I don't know where it is constantly".
3. Federation ships should follow 'better' / 'improved' behaviour than traditional ships due to sheer size/FP in terms of aggression and should not be weighed down by if the enemy is Overwhelming to them (not the player, I mean e.g. Crisis) like a normal empire behaviour may otherwise do.
Relates to 2 but this gives importance onto the AIs usefulness as being a president, I don't want to depend on me being president to make an impact on a war, I'm as happy being the AI's wing man.
4. Federation fleets are awful to manage along your own fleets, creating a lot of clutter. They deserve their own Outliner section or even menu.
All being said - I'm more than happy to go to the effort of reproducing those steps where I can but it would be nice to know if they are already 'acknowledged'.