You could make an argument for Stash fitting Prosperity merely for the fact that it is a special treasure.
Black Market is perfect for Cornucopia, as it promotes variety.
I suppose Envoy has to go in the base set, as it doesn't particularly fit the others.
Stash lets you set up a future turn, which is how it fits Seaside, which it's an outtake from. Black Market was in Seaside on the grounds that it reached outside the game, which was like reaching outside the turn taken to extremes.
Envoy gives an opponent a choice, thus fitting Intrigue, which it's an outtake from.
Here's how I count the themes:
Intrigue:
10 Choices: Pawn, Masquerade, Steward, Swindler, Wishing Well, Baron, Mining Village, Minion, Torturer, Nobles
7 Also choices, but less unique: Courtyard, Secret Chamber, Ironworks, Scout, Saboteur, Trading Post, Upgrade
4 Victory cards: Great Hall, Duke, Harem, Nobles
5 Cards interacting with Victory cards: Baron, Ironworks, Scout, Duke, Tribute
4 Off-theme: Shanty Town, Bridge, Conspirator, Coppersmith
Seaside:
8 Duration: Haven, Lighthouse, Fishing Village, Caravan, Merchant Ship, Outpost, Tactician, Wharf
9 Top of deck: Native Village, Pearl Diver, Lookout, Navigator, Pirate Ship, Sea Hag, Treasure Map, Ghost Ship, Treasury
3 Other other-turn: Embargo, Smugglers, Island
5 Off-theme: Ambassador, Warehouse, Cutpurse, Salvager, Explorer, Bazaar
Alchemy:
12 Potion-related: Apprentice cares if it's in the cost and Herbalist can put a Potion on your deck for reuse, so, the whole set.
5 Actions theme: Transmute, Vineyard, Scrying Pool, University, Golem
10 Useful in multiples: Everything but Herbalist and Possession
0 Off-theme
Prosperity:
8 Special treasure: Loan, Quarry, Talisman, Contraband, Royal Seal, Venture, Hoard, Bank (Platinum)
7 Treasure interaction: Counting House, Mint, Mountebank, Venture, Grand Market, Hoard, Bank
5 Non-attack player interaction: Trade Route, Bishop, City, Contraband, Vault
3 VP tokens: Bishop, Monument, Goons
8 Expensive: Goons, Grand Market, Hoard, Bank, Expand, Forge, King's Court, Peddler (Platinum, Colony)
3 Off-theme: Watchtower, Worker's Village, Rabble
Cornucopia:
5 Care about variety: Menagerie, Harvest, Horn of Plenty, Hunting Party, Fairgrounds
4 Provide variety: Remake, Tournament, Young Witch, Jester
4 Off-theme: Hamlet, Fortune Teller, Farming Village, Horse Traders
Hinterlands:
9 When-gain/buy: Noble Brigand, Nomad Camp, Cache, Embassy, Ill-Gotten Gains, Inn, Mandarin, Border Village, Farmland
4 Other interact with gain/buy: Duchess, Fool's Gold, Trader, Haggler
7 Victory/Treasure/Reaction: Fool's Gold, Tunnel, Silk Road, Trader, Cache, Ill-Gotten Gains, Farmland
4 Interact with Victory cards: Crossroads, Duchess, Fool's Gold, Silk Road
8 Card filtering: Oasis, Oracle, Jack of All Trades, Cartographer, Embassy, Inn, Margrave, Stables
4 Off-theme: Develop, Scheme, Spice Merchant, Highway
Some of the various off-theme cards do connect up with their sets in significant ways. Rabble is an attack that promotes Colonies - you want to wait on buying VP cards to be hurt less. Hamlet supports Menagerie and the excised "hand theme" of Cornucopia; Horse Traders also fits the old theme. Develop is slightly-less-than-instant gratification.