We have a pool of troops, we want these to be equally distributed between planets. Battalions are auto distributed each turn (ignore distance, transport, etc) in order to defend planets.

You have 2 planets and 1,000 battalions. All these are on the 1st planet.

Another case: you have 100 planets and 1,000 battalions, again all on 1st planet.

Yet another case: you have 100 planets and 50,000 battalions, again all on 1st planet.

At what speed (formula) should these be redistributed?

* Percentage based on total battalions? But then if you send 5% out of 100 battalions it will take ages for them to reinforce a planet significantly (if we assume there should be 50 battalions per planet) and if you send at 5% while having 100,000 battalions you will basicly fully reinforce all planets in one turn which is too fast.

* Fixed quantity based? Like a planet can receive maximum +100 battalions per turn?

* Mixed model? Like +5% of total battalions OR +100 battalions, whichever is higher/lower?

You don't produce battalions, you get them for free based on population (recruits), you produce only weapons.

Is this scenario feasible? How many battalions can you produce in one turn on single planet? Or what other scenario can produce such situation that in one turn you are going from single planet with 50k battalions to 100 planets without any additional ones?

The thing is, it's hard to predict how many troops per planet there are (especially when population - recruits - can grow and shrink) at various stages of the game. So, I have trouble determining if +100 is too much or not enough. Plus fixed has a nasty pacing effect, if at the beginning you have 100 per planet then you get a planet reinforced in 1 turn while at late game if you have 1000 per planet it would take 10 turns...

Is it a fluid like model, where distance comes into play? Ie, to get to Planet X from Planet Z, you have to pass through Planet Y?

You could also tag planets with a incoming priority tag

Perhaps an I/O based off population. Allowing each planet to send out 50% and receive 50% of their max recruitment factor each turn. Making sure that 50% is the total number of troops sent or received, not a per planet.

But then the player can micro-manipulate this by adjusting planet defence priority for one turn and then back after the planet got fully reinforced...

I would consider simulating travel times and intermediate locations for reinforcements moving from planet to planet, even without simulating the spaceships that are used to transport them.

A model in which, every turn, there are convoys transporting reinforcements in certain deep space locations and currently en route to a certain place allows more realistic decision making and more meaningful policies. For example:

• You can define a virtual "road network", which also implies distances between planets: quite a richer topology than with instantaneous travel.
• When does planet X need reinforcements? Which reinforcement convoys can get there on time? Of these, which ones should be rerouted to planet X and which ones are needed elsewhere? It becomes a fairly simple constraint satisfaction problem.
• Apart from troops actually needed for planet duty (exploration, maintaining order etc). most troops would be needed to fight invasions and they would "hover" in convoys that can reach any of a few nearby planets quickly enough to react to attacks (coming from similarly slow fleets). Only remote planets would have large forces committed exclusively. Planets would form clusters sharing deep-space troop reserves; depending on sensor quality and enemy speed, clusters could be mostly overlapping, mostly single planets, or something in between (and more varied).
• Especially if you treat troop transport starships as a free unlimited resource, there is a clear guideline for deciding how many troops leave planets: as many as possible, because sharing them with another planet is strictly better than leaving the other planet less defended.
• There's also a clear guideline for where to send them: towards the parts of the empire with less troops and more threats, for example maximizing the size of the enemy fleet required to conquer the weakest planet.

I can't quite see why fortification should depend on population on the planet.

Player will most likely have some sort of overproduction