What are the rules in each version of D&D that specifically discuss making higher or lower-powered heroes, at level 1, based on the type of campaign?
I recall that the 3e DMG makes mention of this when determining point-buy systems for ability scores, and there is also a discussion about making very high-powered heroes as gestalt characters in the UA.
What else was out there in the different editions (for rules suggestions for different power levels of campaigns, starting with character creation)?
In most cases, that's done by adjusting the method for generating stats.
The 1st Ed DMG includes a whole bunch of die-rolling methods for generating characters that are more or less generous than the default (which, IIRC, is 4d6-drop-lowest). There are then some further methods given in "Unearthed Arcana". I don't think there is a 'true' point-buy method amongst them, but I stand ready to be corrected.
The 2nd Ed PHB includes 7 methods, with the default being 3d6 in order (!). Indeed, the 2nd Ed DMG gives DIRE WARNINGS that if you dare to use 4d6-drop-lowest you're liable to break your campaign.

Again, I don't recall there being any 'true' point buy method in there - the closest you get is one where you roll 7d6 and then assign those values to the stats. 2nd Ed is the only edition change ever to
reduce the power of PCs, and it also featured "The Complete Book of Priests", the only supplement I've ever encountered that did the same.
3e you've already mentioned. I'm not aware of any 'official' variants in 4e or BECMI D&D, but again I stand ready to be corrected.
Once we get into house rules, there are obviously many options. In 3e, this seems to take the form of just varying the number of points in point-buy, although quite a few do "4d6, count 1's as..." or similar. It's also quite popular to give one or more bonus feats at 1st level.
And, of course, you can vary the power level by adjusting starting funds or by assigning starting gear, although I'm not aware of any official rules for doing so.
Also, it seems that folks favored rules that raised stats for high-powered campaigns, but did not use rules that lowered stats for low-powered campaigns.
Yep, arguing for raising the power level never seems to be an unpopular option. Arguing for reducing it, or even for just maintaining it, is a much harder fight.