Forgive me if this is common knowledge / expected, but while paying close attention to my fleet stats while reorganizing them, it seems that having any Hero, regardless of any skills, assigned to a fleet grants the entire fleet an additional +20% Health regen per turn?  It seems to take effect regardless of whether the fleet is in friendly, neutral, or enemy territory.  This came as a bit of a surprise to me, because unless I'm forgetting something, I don't believe the game notifies the player of this feature.  It certainly is a huge benefit, seeing as by default fleet regen is just 0% in enemy, +5% in neutral, and +10% in friendly territory.

EDIT - BONUS QUESTION:

While I'm at it, does anybody know the mechanics behind fleet manpower refilling? I'm trying to work out how exactly some of the Hero ability which do stuff like "+40% manpower refill rate on fleet" work exactly. The only stuff I know for sure is that in enemy territory, fleet manpower doesn't refill at all, while in neutral / friendly territroy, it does refill. However, I don't know what exactly governs how much it refills per turn, what the maximum limit to how much it can refill per turn, whether it works by % of max fleet manpower or some set amount of manpower per turn, etc.

Relatedly, I do know from a bit of testing that, for example, the "+20% system manpower per turn" bonus that comes from Dictatorship's "Militarist Propaganda" works by taking whatever the current incoming system manpower refill per turn is, then generating 20% of that figure as "free", bonus manpower that doesn't draw from your empire reserves / food supply. However, I still don't know what exactly governs how much system manpower refills per turn in general.

UPDATE:

Whoops!  I hadn't actually realized you could look through your quest log to see previous rewards. It was "Endless Augmentation Factory," a reward for one of the Craver main quests.

Well, I suppose my only complaint would be that I wish there was a nice "one stop shop" page that listed all current effects on your empire, similar to how the Quest tab lists all temporary Quest effects, and the Empire screen lists all innate and Assimilated faction traits. Apparently, forgetful people like me may not remember what bonuses we have after returning to a 3 month old savegame :)

Although I'm still curious if anybody know more about how fleet manpower refilling works normally.

Well, I'm only noticing it just now, so perhaps there is some special circumstance I'm not of aware that triggers it.  Can anyone else confirm / deny if Hero fleet health regen works like this?  I don't seem to have any empire traits / quest effects that would cause this.  Also, while I'm here, I have a bonus question about fleet manpower.

Ah yes, you are correct!  

My mistake, I hadn't actually realized you could look through your quest log to see previous rewards. It was "Endless Augmentation Factory," a reward for one of the Craver main quests.

Well, I suppose my only complaint would be that I wish there was a nice "one stop shop" page that listed all current effects on your empire, similar to how the Quest tab lists all temporary Quest effects, and the Empire screen lists all innate and Assimilated faction traits. Apparently, forgetful people like me may not remember what bonuses we have after returning to a 3 month old savegame :)

Although I'm still curious if anybody know more about how fleet manpower refilling works normally.

Yeah, unfortunately it neither shows up anywhere in my Tech screen, nor anywhere on my Empire summary (although as you say, it does list default traits and assimilated traits).  I agree it would be a very convenient & logial place to put such information, if they're thinking about future updates :)  Possibly throw in some other odds  & ends such as current # of depleted planets in Empire, or what the current effective health & damage bonuses are for your troops due to all bonuses, etc.