The bonus tile does nothing for the manufacturing capital. At least, that is what has been posted here many times, and I believe I confirmed it by test myself several years ago.

The same non-effect applies to the research bonus tile and the research bonus structure, IIRC. OTOH, the political capital effect is boosted by placing it on either an infulence bonus tile or a morale bonus tile. That is, its influence is doubled on the influence bonus tile, or its morale bonus is boosted on the morale bonus tile. (I always place it on the latter on my homeworld, as it helps me keep taxes up without too bad an impact.)

The power plant is multiplicative with the manufacturing capital but no bonus tile helps it more either.

Thus, a 7X manufacturing tile can be boosted twice, once my the capitol and the second time by the power plant.  (DA)

YAQW!

I always reserve a morale tile on my homeworld just for that!  It is one reason I rush to Democracy, just after the rush to Trade for the Economic Capitol (which I also place on the homeworld because it will usually have the highest pop until late game).

BTW, the exception on locating the Eco Capitol is when a better planet than your Homeworld is just one hex away from the start planet, letting you do zero turn population movement.  In that case, I shift most of the population over and then put the Eco Capitol there.  That situation happens about one time in four (roughly) if you structure your game set-up conditions a certain way.