I was waiting for Bulbapedia to finish creating the pages for the new Pokemon as they're usually more meticulous with Pokemon origins. Though I can quickly go through each to see what design basis I can pick-up/heard about/Bulbapeda have already described:
Grookey Family: Monkey, Gorilla, Drummer
Scorbunny Family: Rabbit, (Soccer) Athlete
Sobble Family: (Veiled) Chameleon, Emo Subculture, Spy
Skwovet Family: Squirrel
Rookidee Family: Blue Tit, Chickadee, Raven, Crow, Black Knight
Blipbug Family: Ladybug/Ladybird, Bookworm, Radome, Flying Saucer
Nickit Family: (Red) Fox, (Masked) Burglar/Thief, Guy Fawkes Mask
Gossifluer Family: Cotton
Wooloo Family: (Jacob) Sheep/Ram
Chewtle Family: (Alligator) Snapping Turtle
Yamper Family: Welsh Corgi, Greyhound
Rolycoly Family: Coal, Mine Cart, Furnace/Forge, Mountain
Applin Family: Worm in an Apple, Wyrm (limbless dragon), Worm of Linton, Amphithere (winged, legless dragon), Drake (wingless dragon), Apple Pie/Turnover
Silicobra Family: Cobra, Anaconda, Shotgun
Cramorant: Cormorant
Arrokuda Family: Barracuda, Pike, Arrow, Torpedo
Toxel Family: Baby (in a diaper), Punk/Grunge Rocker, (Electric/Bass/Air) Guitarist
Sizzlipede Family: Centipede, Shocking Pink Dragon Millipede, Omukade
Clobbopus Family: (Boxer/Blue-Ringed) Octopus, Boxer, Jujitsu
Sinistea Family: Poltergeist, Tea Cup, Teapot
Hatenna Family: (Party/Witch) Hat, Antenna, Witch, Witch Tower, Witch's Ladder, Rapunzel (& Dame Gothel)
Impidimp Family: Imp/(Hob)Goblin/Gremlin/Boggart, Redcap, Bugbear, Troll/Ogre/Grendel (Beowulf)
Galarian Zigzagoon Family: European Badger, Glam Rock Star (specifically Kiss)
Galarian Meowth Family: Viking (notably a Berserker), Norwegian Forest Cat, Viking Sword, Freyja's Cats (Bygul & Trjegul)
Galarian Corsola Family: Bleached Coral
Galarian Farfetch'd Family: Knight, Onion Knight, Sir Lancelot/the White Knight
Galarian Mr. Mime Family: Tap Dancer, Vaudeville Actor/Comedian (specifically of Charlie Chaplin's "The Tramp" character)
Galarian Yamask Family: Runestone
Galarian Ponyta Family: (No basis change from what I can tell, Ponyta become a unicorn but Rapidash was already one)
Galarian Weezing: (Stovepipe) Top Hat, Smokestack
Galarian Darumaka Family: Snowman, Yeti
Galarian Stunfisk: Foothold Trap
Milcery Family: Drop of Milk/Blob of Cream, Whipped Cream, Wedding Cake
Falinks: Spartan (Helmet), Phalanx
Pincurchin: Sea Urchin
Snom Family: Domestic Silkmoth
Stonjourner: Stonehenge
Eiscue: Penguin, Ice Cube
Indeedee: Housekeepers, Butlers, Maids
Morpeko: Hamster, Guinea Pig
Cufant family: Elephant, Digging Spade, Maharajah, Excavator, Trencher
Galar Fossils: Misassembled Fossils, "Velociraptor", "Dunkleosteus", (since the bottom half can be a number of prehistoric animals I'm not going to bother trying to figure out what they are)
Duraludon: Building (specifically London's tallest building, The Shard), Mechagodzilla
Dreepy Family: Diplocaulus, Missile, Stealth Bomber
Zacian & Zamazenta: Wolf, Sword, Shield, King
Eternatus: Space Dragon, Thanatos
Does anyone have any additional suggestions? Notably animals/objects/concepts/mythical creatures that are on a Repository List so I know to remove them.