Brief overview:
This particular hybrid genre is quite rare to find and very enjoyable for me. I think it can largely be credited to Ratchet & Clank for trendsetting and inspiring all the rest (even Jak 2 had used some of Ratchet's code after Jak and Daxter [1]: The Precursor Legacy didnt have any weapons). There are some older games that might have inspired Ratchet & Clank, such as Blasto, which will also be listed here. But mostly I'm focusing on games that replicate a similar style as the Ratchet and Jak series, sometimes on purpose. Please let me know if you have any additions to the list.
The List (main):
▪︎ Ratchet & Clank (series) ▪︎ Jak and Daxter (series) ▪︎ Protodroid DeLTA ▪︎ Akimbot and Pumpkin Jack (same dev as each other) ▪︎ Tamarin ▪︎ Automaton Lung (& sequel Automaton Heart demo) ▪︎ GearGrit (and the devs' other game Fadeout kind of) ▪︎ Cloudbuilt ▪︎ Onirism ▪︎ Metal Arms : Glitch in the System ▪︎ Ruff Trigger : The Vanocore Conspiracy ▪︎ Donald Duck PK (AKA PK : Out of the Shadows) ▪︎ SpongeBob SquarePants: Plankton's Robotic Revenge (yes, this is really a 3rd person shooter) ▪︎ Oddworld: Stranger’s Wrath ▪︎ Shadow the Hedgehog ▪︎ Spy vs Spy ▪︎ Blasto
I've heard recommended but can't verify if they fit the bill or not:
▪︎ Jet Force Gemini ▪︎ Stitch: Experiment 626 ▪︎ Smarties: Meltdown ▪︎ Insecticide ▪︎ Dr. Muto ▪︎ Destroy All Humans! (series) ▪︎ Robots ▪︎ One ▪︎ MDK (series) ▪︎ Earthworm Jim 3D ▪︎ Buzz Lightyear of Star Command ▪︎ Blinx : The Time Sweeper ▪︎ Cryght ▪︎ Mega Man Legends ▪︎ Fur Fighters
Similar gameplay elements either continuously or occasionally:
▪︎ Sly Cooper (series) ▪︎ Ty the Tasmanian Tiger (series) ▪︎ Rayman (the 3D games) ▪︎ Skylar & Plux ▪︎ Spyro the Dragon (series) ▪︎ Super Mario (series) ▪︎ Crash Bandicoot (series) ▪︎ Astro Bot (series) ▪︎ *Psychonauts (series) ▪︎ Futurama ▪︎ Family Guy Video Game! ▪︎ Jumping Flash ▪︎ The Gunk ▪︎ Splatoon (series) ▪︎ Sunset Overdrive ▪︎ Returnal ▪︎ ReCore ▪︎ Lost Planet (series)

You can try this
https://www.mobygames.com/game/genre:behind-view/
In the genre filter you can add Platform and Action and Shooter
Thanks, but I am looking for 3D platformers only. Not 2D platformers. Often they're lumped together which is sad. This resource would be useful in theory, but after putting in "third person", "platform" and "shooter" (there's no separate option for 3D platformer vs 2D platformer), I'm getting many results of games that don't seem to match what I'm looking for, including 2D games like Cartoon Wars: Gunner. However I did forget to mention Uncharted as having somewhat similar gameplay elements, although I wouldn't consider it a 3D platformer. I guess Zapper very very loosely meets some of the criteria, but it's more like a top-down Frogger-like game with some.. zapping. It's weird that there doesn't seem to be a way of differentiating games with 3D graphics from 2D graphics in general on this site. I guess I can check all of these hit-and-miss results one by one, but word of mouth recommendations probably work better here, especially for obscure games. Notably, many of the games I listed (such as Akimbot, one of the prime examples) aren't showing up under these filters even though they meet the parameters. I also forgot the upcoming game Pragmata is giving vibes but it's not showing up on that site under those filters anyway.
Too bad, but I guess that's what happens when a site is crowd-edited. Changing the genre might not be something people stop to change. Pragmata and Akimboy are just listed as a "Behind View" "Action" games. The filter uses AND operators which means that users would need to mark up games with all 3 tags to work that way.
Fun to see that 2D side scrollers are considered 3rd person by some users though!