A lot of that is probably backdated to PP1 where by the time Squadrons came in, virtually no-one did Powerplay except for the modules. How much it changes we'll see over time.
In Powerplay 2... for the squadrons:
- there is no penalty to pledging a squadron to a Power, and you appear to be able to change or revoke that pledge later
- there is no requirement for squadron members to pledge to the same Power (or any at all) as their squadron and no penalty for them picking a different one
- if you do pledge to the same Power as your squadron, your earned merits also boost your squadron's Powerplay leaderboard position [1], and even if you're not aiming for a leaderboard trophy you can use this to get a rough idea of the total merit-earning power the squadron can deploy.
In terms of interactions with the BGS:
- there's a lot less direct interaction - Powers shouldn't in general have a preference for which faction controls a system, and most Powerplay activity in a system is neutral or positive for the controlling faction. So if you want to just do BGS and ignore Powerplay, individual members can pledge to whoever they like (but might find it easier to pick a power which is local to your faction's space) and the only real effect on the BGS from Powerplay seems to be "there are a lot more players around in general so the BGS is noisier; groups used to being the only people in their systems have had a bit of a shock"
- if you want to do both BGS and Powerplay as a squadron then you will probably find it useful to have a single Power across all of your systems (which you'll likely need to work for if you've expanded much!) and have everyone in the squadron either pledged to that power or neutral. But if you do that you'll get a bunch of useful synergies where a lot of your BGS work also gets you Powerplay merits (either directly, or by providing convenient opportunities to grab some along the way) and reinforces your Power in your systems / helps kick out other Powers.
(My squadron - admittedly, just a personal one I've set up for tracking purposes and not one I expect anyone else to join - is pledged to a Power but not to a minor faction, so goes the other way)
[1] Based on this, the number of squadrons with a Powerplay affiliation matching at least one of their active members seems to have gone up by about 4x with the introduction of PP2.