Necroposting this even though it is still on the front page.
This was posted August 2021.
Since then we have two expansions, Allies and Plunder, and Seaside/Prosperity/Hinterlands 2nd editions.
Looking at Allies, there are 31 kingdom piles.
Of the normal piles, Bauble and Galleria grant buys.
Importer, Carpenter, Modify, Specialist, and Swap either gain or remodel cards.
Of the split piles:
Town crier and Acolyte can gain specific cards.
Sunken Treasure and Conjurer can gain other cards.
Distant Shore and Territory I guess also gain specific cards.
But the wildcard in Allies are the titular Allies, many of which offer gains (or effects equivalent to gains) under varying conditions.
As far as ordinary buys go, that's only 2/31 piles granting general +buys, which is very low, but Allies offers many other ways to gain cards without +buy.
Plunder:
The Loot deck in Plunder has 22/30 cards that offer +buy or an extra gain (Hammer).
This means that 6 Kingdom cards, 5 events, and 1 trait in Plunder offer the player additional buys by proxy (plus Jeweled Egg and Sack of Loot already offer +buy on their own).
With non-loot-related cards, Abundance, Rope, Buried Treasure, Figurine, and Mining Road provide buys.
Tools, Cabin Boy, Enlarge, Quartermaster, and Silver Mine either gain or remodel cards.
King's Cache and Flagship can also (conditionally) provide, but they require another +buy card.
Finally, Fawning, Friendly, Nearby, and Rich offer additional gains/buys, with Nearby specifically explicitly providing a buy.
11/40 kingdom cards in Plunder thus introduce explicit +Buy cards to the set, which is a very high ratio (27.5%) compared with the 3/26 in the base set.
Now, let's look at 2nd editions:
Prosperity:
Tiara and Collection are explicit +Buy cards, War Chest and Anvil also offer gains.
Removed were Trade Route, Contraband and Goons, which each provided +1 buy (Contraband having a drawback). Talisman could also gain a card.
In pure '+Buy' count, it is a complete wash, as Prosperity 2E dropped 9 and added 9 cards.
Seaside:
Astrolabe is a +Buy. Blockade and Pirate can gain cards.
Explorer was removed (who could gain Silver/Gold), the other removed cards were neither gainers nor +buy.
The net result is a slightly better +buy average than before.
Hinterlands:
Nomads, Cauldron, and Souk
Weaver, Berserker, and Wheelwright gain cards.
Nomad Camp is the only +Buy removed. Noble Brigand could gain cards, and both Cache and Ill-Gotten gains gained cards, but those were copper.
this gives Hinterlands a net +2 Buy cards.
I'm not set up to completely crunch the numbers as faust did in 2021, but I have a hunch that in a random kingdom with 2 extras (Traits/Events/Projects), and other extra set-up things like a random Ally if one or more Liasons are chosen, the odds of a +Buy kingdom must have improved.