The Wiki essentially says a bunch of fanfic here, in the absence of any official word on the matter.
It's basically a mess [1].
- both minor factions and Powers can be aligned to superpowers, but don't have to be
- Power alignment to a superpower does absolutely nothing in Powerplay 2 (it decides which modules you unlock at the early ranks, and even that's largely inherited from Powerplay 1 for convenience)
- minor faction alignment to a superpower does very little
- in Powerplay 2 there's even less connection than in Powerplay 1 between minor factions and Powers (and in neither did a superpower mismatch do anything)
Leaving aside Grom (as a player-shaped Power, they're not necessarily going to fit any particular theme), then Antal and Li Yong Rui and Delaine represent particular influential organisations outside the superpower structure (Utopia, Sirius Corporation, the Pegasi Pirates)
- Utopia has no associated minor factions
- Sirius has several associated minor factions
- the Kumo Crew has an associated minor faction now because of a story requirement for it to own a station or two at one point, but got through the first several years of the game quite happily without one
- Yuri Grom was created via the Dangerous Games so there is an associated PMF in their case, which existed first, but of course only the one.
Most independent minor factions aren't in any way associated with any of those initiatives, nor do they need to care about them to retain their independence.
Similarly in the superpowers, the various Powers represent major internal power blocs, but none of them have associated minor factions added by Frontier (some have one or two thematically associated PMFs). In theory each superpower minor faction also is probably sympathetic to or part of one of those power blocs ... but there's no indication in-game of which ones are for which, nor does it affect Powerplay in any way.
So for example, the current CG is taking place between Arissa Lavigny-Duval and Archon Delaine.
- ALD is represented by the miscellaneous Imperial faction which happens to control the system (but if Torval had led the attack, they'd have worked for her instead)
- Delaine is represented by their associated minor faction (as one of the few Powers to have one) which has been Frontier-inserted into the system for the CG
- but the system itself started the game as Federal, and still has The Sarge, a Federal-aligned engineer who requires Federal rank to unlock, working perfectly happily there
- and the system contains 2 other Federal and 4 other Independent minor factions, any of which could take control of the system without affecting Powerplay at all.
There's not really a way for Frontier to sort this out without making extremely major changes to all three of superpowers, powers and minor factions (probably involving abolishing at least one of them entirely!) so in practice they need to be treated as three entirely unrelated things.
[1] And colonisation makes it even more confusing. With the hyper-expansion allowed by colonisation, the largest individual minor faction now controls more systems than the largest power, and also more systems than the entire Alliance controlled pre-colonisation. Yet their status is still "minor faction", not Power or Superpower.
There's a world where Powerplay was never about territory... instead the territorial games were an inter-superpower affair, indirectly affected by Powers.
Minor Faction interactions = Tier 1 NPCs[1]
Powers = Tier 2 NPCs[2]
Superpowers = Tier 3 NPCs
Very spitballed, repeated successful, short term interactions at Tier 1 for the same factions curries favour with a Power, based on the type of actions and the superpower it supports. That introduces you to more rewarding, longer-term objectives offered by the Power representatives which drive their particular agenda within the superpower, and equally allow them to exert influence against the other powers by-proxy through Superpower-level conflict (generally, grey-zone conflict, but can just become outright warfare). Eventually, this turns into offers direct from representatives of a superpower which are much longer term, and open the door to more direct and rewarding activities that pursue more direct outcomes against a superpower.
Critically... the superpowers themselves are represented
by a power generally... so in practice this means the Independent powers are in fact mini-superpowers in their own right.
Towards that end, minor factions are your day to day BGS effects, Powers represent major influence effect operations couched around the main playstyles, while Superpowers represent the conflicts played out by those influence effects.
So, let's say you were working with the Empire, specifically favouring activities in giving strength to ALD as the current head, this would look like:
Tier 1 - Various imperial factions, Tier 2 - The Imperial Court, Tier 3 - Office of the Emperor (ALD)
But if you favoured Patreus, your interactions would be with:
Tier 1 - Various imperial factions, Tier 2 - The Imperial Fleet, Tier 3 - Office of the Emperor (ALD)... noting this could change if Patreus (Office of the Fleet Admiral?) became the main source of influence for Imperial activity.
Meanwhile, for an Independent, if you were supporting independents with Antal-style activities, you'd go:
Tier 1 - Various independents, Tier 2 - The Utopia Movement, Tier 3 - Representatives of the Simguru (Antal)
And then, because territory is owned by the Superpower, not the Power, you
can introduce or remove powers as they curry favour (or don't) without disrupting the current state of play... it's simply a new vector to shape your activities around for influence effects.
Ofc, before anyone goes "yes but XYZ", obviously this isn't a fully fleshed out suggestion, and there's a lot of gaps in this which, while the solutions might not be presented here, do have solutions that are much more tenable than trying to resolve some of the same issues currently facing PP2.
Tying it all back to this proposal... it's no longer about "which flag you fly"... it's about who you support with your actions, whether you intended to or not.
[1] Actually, the mission boards would be Tier 0, and Tier 1 the on-foot contacts in Odyssey
[2] This would also be Engineers and perhaps other notable individuals.