After my semi-regular (at least every other year) playthroughs of Rareware's Banjo-Kazooie and Banjo-Tooie, I looked up more development info and my hot take is that contrary to what is usually stated, Project Dream did not become Banjo-Kazooie. It became both games.
......And Donkey Kong 64, sort of.
Here is the world map for Project Dream:
It's a group of islands with many different levels based on varying terrain: Jungle, Beach, Temple, Water, Forest, Mine, Houses, Fantasy, Swamp, Spooky, Lava, Ice, Desert, Factory, Fairground, Big City, Eskimo Camp, Bear Cave, Oasis Caravan, Groves, and Pirate Bases.
When the game transformed into Banjo-Kazooie, the developers still stuck to the same ideas for levels, although they were now accessed through the overworld of a witch's castle. They began with the Jungle level which ended up changing into a jungle mountain terrain, hence its name of "Mumbo's Mountain". The Beach level was Hammerhead Beach, but was later changed to Treasure Trove Cove. Fungus Forest was to be the Forest level, but the addition of a whale ended up causing them to recenter the level around it, punting Fungus Forest to later, and then the Whale level was further modified to become mechanized and taking place in a sewer. The Swamp level was Bubblegloop Swamp, the Ice level was Freezeezy Peak (with aspects of Eskimo Camp), the Desert level was Gobi's Valley (with aspects of Oasis Caravan), the Spooky level was Mad Monster Mansion, and the Water level (with aspects of Pirate Bases) was Rusty Bucket Bay. In addition, a Lava level, a Mine level, a Fairground level, a Fantasy level and a Seasons level (featuring several Houses) were planned in addition to the aforementioned Fungus Forest. But all of those levels ended up scrapped for time except for the Seasons level, which was now combined with the Forest level to make Click Clock Woods. And that, of course, is the finished version of Banjo-Kazooie we have.
Banjo-Tooie began development immediately after, and the planned levels were Dinosaur, Fairground, Mine, Mushroom, Factory, Ice Caves, Sunken City, Lava Island, and Castle. Many of these were reworked versions of levels they scrapped: the Lava, Mine and Fairground levels are all here, and despite what you might be thinking, the Mushroom level was actually a reworked version of the Fantasy level, not Fungus Forest (more on its fate later). Dinosaur is a new level based around the fact that dinosaurs were meant to be in Project Dream, particularly the giant Stomponadon who was so big all you saw was his foot. Sunken City was also based in concepts for the Water level of Project Dream that included Atlantis as a setting, Ice Caves would be more true to what was envisioned in Project Dream as opposed to the more Christmas-themed Freezeezy Peak, and Factory was also a level idea from Project Dream. Castle, of course, was the new lair for the Final Boss, Gruntilda.
Project Dream was not done influencing the game's development, as Temple, another level concept, was later brought in to be the first world (discounting the tutorial world Spiral Mountain and overworld Isle o' Hags), and it also included Jungle and Groves elements. Mayahem Temple even used a remix of music that was composed for Project Dream, as did the Atlantis section of what was now called Jolly Roger's Lagoon (and as the name suggests, Pirate Bases are also an influence in it). Mine became Glitter Glutch Mine, Fairground became Witchyworld, Dinosaur became Terrydactyland, Factory became Grunty Industries, and Mushroom become Cloud Cuckooland (with gelatin replacing the mushrooms). Finally, to cut corners, the Lava Island and Ice Caves were merged into Hailfire Peaks, and Castle was scaled down from a full world into a smaller area, Cauldron Keep, which is just a tall tower.
But wait! Donkey Kong 64 was being developed by Rareware at the same time as these two games! Its levels were Jungle Japes (another mountainous Jungle themed level), Angry Aztec (a Temple level crossed with a Desert level), Frantic Factory (a Factory level), Crystal Caves (an Ice level, which also might have been a reason why Hailfire Peaks ended up happening in Banjo-Tooie), Fungi Forest (a reworked Fungus Forest, now with a day/night cycle added), Gloomy Galleon (another Water level crossed with Pirate Bases), and Creepy Castle (a Spooky level crossed with the Castle level originally planned for Banjo-Tooie).
So in the end, basically every environment except for Big City, which no longer would have fit, crafted for Project Dream was ultimately utilized for Rareware's Nintendo 64 games. Even its intended antagonist, Captain Blackeye, got to cameo in Banjo-Tooie's Jolly Roger's Lagoon!
Never give up on your dreams, folks. In some form or other, they can end up coming true.