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One strategy I've seen is to remove all the support units from hqs, then reassign them to units or hqs as needed. However, this incurs a 50% CPP penalty for being reassigned according to the manual - so assign the SU to STAVKA and then back to an HQ should drain a lot of CPP, id imagine around 60% (i cant check due to thanksgiving travels) How important is this in the first handful of turns? Many support units are there for killing power, not CV; as I understand the manual, CV seems to be the biggest combat effect of CPP. Are the secondary effects of CPP of SUs impactful? Mainly, I'm thinking about the movement effects. How does CPP of SUs impact movement?

CPP does not affect movement, as well as any SUs

Stamb wrote: Fri Nov 25, 2022 10:39 pm CPP does not affect movement, as well as any SUs

Is this a new thing? The manual states: "Note that in addition, CPP can have a substantial
effect on the MP of a unit (22.1). If the unit passes a test
comparing CPP to a dice roll (higher the CPP, the greater
chance to pass) then the movement allowance will not be
affected by fatigue, or missed initiative and administration
tests. It will still be affected by shortages of fuel, supply or
trucks or having been attacked in the previous turn."

So is your question about CPP -> SU -> Movement? Or CPP -> SU? Or SU managing?

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SU-CPP -> Movement:

ringhloth wrote: Fri Nov 25, 2022 8:55 pm How does CPP of SUs impact movement?

Living Manual 1.18 p.353 wrote:Though they have no organic movement capability, support units will consume supplies and fuel and gain fatigue when units to which they are attached are moved. They will also take combat and non-combat losses and suffer retreat attrition along with the unit to which they are attached.

CPPs may affect MP-regain as you quoted, but not for SUs, since they don't have MPs. The CPPs may impact some minor calculations for SUs but I'd say you can neglect them and therefore CPPs on SUs are mainly increasing CVs I'd say (as you already noted).

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SU-CPP -> Combat/Supplies:

Living Manual 1.18 p.402 wrote:In addition, CPPs affect the chances of passing administrative rolls for resupply and to reduce fatigue when in contact with the enemy. In addition, the chances of Support Units being committed and the effectiveness of artillery are also influenced by the number of CPP a unit possesses.

Living Manual 1.18 p.409 wrote:The chance of support units being committed can also be increased by the level of fortification in the defending hex. Equally the number of Combat Preparation Points of the units involved in the combat will affect the chances of support units being committed and the effectiveness of any artillery allocated (23.2.3).

From how I read this, this CPPs is meant to be the CPP of CUs, not SUs. Therefore as said before, CPP gives CV not much more,....I am not sure about the actual scale/impact of the supply/artillery/fatigue effects.
I guess the "reduce fatigue when in contact with the enemy" effects are the ones you can find in 23.8.1. (if/who/how a ground element engages).

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SU-CPP -> Management:
I leave the SU management part to veterans since I could only repeat what I've read/learned by others without seriously figuring it out by myself.

from my limited POV:
Just as a general note, in the first few turns you either overrun or being overrun, therefore the SUs>CPP>CV change/impact is minor (I'd say). So I'd suggest to reorganize as earyl as possible and give every Corps a dedicated/locked amount/kind of SUs and keep the "special SUs" (flamethrowers/heavy artillery etc.) for assignments as needed.

ringhloth wrote: Fri Nov 25, 2022 10:50 pm

Stamb wrote: Fri Nov 25, 2022 10:39 pm CPP does not affect movement, as well as any SUs

Is this a new thing? The manual states: "Note that in addition, CPP can have a substantial
effect on the MP of a unit (22.1). If the unit passes a test
comparing CPP to a dice roll (higher the CPP, the greater
chance to pass) then the movement allowance will not be
affected by fatigue, or missed initiative and administration
tests. It will still be affected by shortages of fuel, supply or
trucks or having been attacked in the previous turn."

my answer was for this question:

How does CPP of SUs impact movement?

When you have combat unit and assign SUs to it then combat unit will have exactly the same amount of MPs as before an assignment of SUs . Maybe on the next turn it will have less MPs if there is not enough freight to supply units in that area, and adding SUs will make situation a bit worse, but typically they do not consume a lot of freight and are well worth it.

as for an affect on a combat/CV then it depends on SUs type:
brigades have pretty serious impact on CV, for example rifle or tank brigades (Soviet side) and some other units for the Axis

and while arty/rockets will not give you much higher CV - it will disrupt enemy, which will decrease enemy CV
pioneers will help with a fortifications and AA vs planes

Better one bird in your hand than 20 in the forrest is my philosofy.