I imagine given the BGS and PP were intrinsically linked for 9 years, Frontier said that the new system would not affect the BGS because that's what they thought would happen. And then when they turned it on...
Things can certainly be literally true - Powerplay's actions have largely been designed not to
intrinsically have BGS effects, or only minor ones, and also to give Powerplay groups no reason to care
which minor factions are present or controlling particular systems - without necessarily describing the full outcomes.
If PP 2.0 is going to be having such a big impact on the BGS through massively increased activities, then the wider implications for those who truly dedicate themselves to it could be pretty severe.
That's the key thing, I think - a big change in
incentives can have a major indirect effect even though nothing in the BGS itself has changed at all. The change back in late 2020 to increase bounty payouts was carefully done
not to change the individual BGS effect of any bounty at all. But the increase in bounty hunting it caused had measurable effects on the overall state of the BGS nonetheless.
About half the Powerplay actions have no BGS effect at all ... but the other half do (or encourage gameplay which might) in such a way that the system controller is most likely to gain influence from it [1].
(To a large extent this is also true of any
non-Powerplay action that a random player might perform in a system, of course. If someone had posted "hey, we think Raxxla is in [one of your systems]" then the rush of players coming to check it out might have done something similar, temporarily. But Powerplay gives players longer-term incentives to go to systems they might otherwise have never visited.)
Actually... I wonder if them removing the limit on player contributions to PP has had some kind of affect on the limit that's normally applied to BGS contributions...
I'm reasonably sure that there is no major
general change to how the BGS works - low-to-mid-traffic systems seem to be behaving normally, the influence levels and patterns out Colonia-way are basically normal despite slightly increased traffic, etc. There have been a few oddities around conflicts seeming to get "stuck" but nothing obvious otherwise.
The BGS limit was never a per-player one anyway (at least not for the sort of activities people were likely to do as "background" activity) so I doubt that's had an effect.
If it's just a change in incentives and player distribution, then as you say it's hard to say it's actually a bug: it may just be a new normal that people need to get used to.
[1] Which, inconvenient as spare expansions can be, is at least better for BGS players than incentivising people to do things which benefit secondary factions and sticking every system into a control war.