Most of the bonuses of that sort are specifically constructed not to also boost your merit earning for the related activities (though I think search and rescue might be an exception where you do get it applied to your merit earning)
However all powers also have their own set of "preferred" activities - which often line up fairly well with their rank bonus - for which you get +50% extra.
So for example as a Kaine supporter I get (up to, depending on rank) 50% extra credit pay for mined goods as a rank bonus. But Kaine also gives me 50% extra merits for using mining as an Acquisition action.
Note that "search and rescue" is currently disabled for merit earning at all (it can still be used to complete weekly assignments) due to some tricky-to-fix exploits. But the credit earning bonus also applies to the "salvage" [1] activity which is still enabled, and as a Duval pledge you'll also get the +50% merit bonus if you use the salvage activity while Undermining.
[1] "Salvage" and "search and rescue" both go through the search and rescue contact in terms of what you do, but are considered separate activities in Powerplay. Salvage is black boxes and wreckage components, search and rescue is escape pods and personal effects.
