I can't speak for the developers' intentions, but Power Play does seem to bring goals to a game that is mostly a sandbox with no "main quest". Perhaps that's what they have in mind?
Last week's merit changes made a greater variety of activities award meaningful merits, so chances are pretty good that you can now help your power while making money or doing things you like.
Yes, bounty hunting is one of the ways you can strengthen a power's hold on a system, although this might depend on which power you choose. Someone compiled a list a few weeks ago.
Do note that while solo players can reasonably progress their way to merit awards, it takes an enormous amount of work to sway control of a system, so that is best done in groups. Unfortunately, most Elite Dangerous groups seem to gather on Discord, which excludes those of us who can't or won't use it.