Are you sure that ships to enemy outpost comes from the system you're sieging?

Pretty sure.

Honestly it feels like "designer" magic where the equations are rebalanced to prevent me from colonizing a fourth system (I'm currently at 3/3 before penalties) instead I'm forced to only capture systems from now on.

I assume every posdible path from lower part is blocked.

You shoul upload a save to allow devs look at it.

Sadly I cannot help more.

No hidden designer magic here:

1. The timer to completion is based only on current Growth stock and current Surplus Food. It does not take food deliveries from your existing colonies into account until they arrive and update the food stock (which is why you can sometimes see the timer making big jumps from one turn to another, especially on outposts with low food production of their own.) If you were not blockading their other systems, they would likely finish the outpost in less than the 3 turns currently shown.
   However, blockading the outpost system itself will change the timer immediately, as the blockade will apply a penalty to food production, so blockading Lupus would be more beneficial in this case (as that would also stop the food shipments in orbit, where you could destroy them).
2. You receive 5 Growth for stealing 10 Food from the enemy outpost because Hissho suffer halved outpost Growth. If this doesn't show in the affinity tooltip, however, that is a bug we need to fix, as it is not supposed to be hidden information. I will check that and file the bug if necessary.

That feels like hidden or misinformation. Stealing 10 food is different from growing or shipping it. But I do understand that food for an outpost is a more heavily abstracted concept.

Just to be clear a blockaded outpost isn't stopped from turning into a colony, just delayed?

Yes, except if food goes to negative value, then you will loss this outpost once foodstock goes 0 (game will tell you how many turns)

"Growth" is a term used for "how much progress does the system make towards the next population unit" (or in this case, the first population unit of the system). It refers to your population growth, not the food they grow in their farms, hydroponics bays, or whatever they may be using. However, your surplus Food is converted to Growth. For most factions this is a 1:1 relationship, but the Hissho suffer halved growth speed on their outposts.

In UI terms, your Food Surplus is the number shown next to the Food icon on the left, your Growth how much the bar below the outpost will advance next turn, highlighted in green. On full colonies, your growth is how much the pop growth circle on the left of the UI fills each turn.

Regarding the blockades, it can be both: The blockade applies a penalty to the Food production, and if that penalty takes the Food production into the negative, the the outpost progress will diminish each turn until the outpost is destroyed. The same can happen from Food being stolen through the military outpost action, which is happening to your outpost in this case.

I'm just seeking extra clarification... there's no interaction of ... manpower. It's just who makes the most abstracted surplus food.

Also if I understand this right. You're saying that while the military action normally grants +10 food, it should be granting +5 food instead due to the reduced grown of outposts.

But in this case it appears that I'm gaining 10 food and losing 10 food. I get+5 from outpost and +4 from exploitation but -9.5 from empire. I'm still trying to find the empire modifier that reduces outpost growth.

Yes, exactly, this is a modifier unique to the Hissho. I believe it is attached to the Honorbound affinity, though it might be attached to the Hissho visual affinity.

On other factions, the conversion of Food to System Growth is straightforward "Surplus Food = System Growth", but for Hissho outposts (not their full-fledged colonies) it is "0.5 * System Food = System Growth"

In your case, you are gaining 5 Food from your basic building, 4 food from the planet, and 10 Food from stealing it from the enemy outpost, for a total of 19. You then lose 9.5 of that to the Hissho modifier. And then the enemy steals 10 Food from you with their own outpost action. (I admit that the order of actions here is a bit odd, as usually penalties like the Hissho growth penalty are applied last.)

Ah. That makes sense. Sorry I couldn't track that math myself.