The jury's out on this one.
Thanks to my friend Jsels for helping plan the route when I couldn't use my PC

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EXPLANATION OF RULES HERE
Banned actions:
When slidekicking off a ledge, the player can input A and effectively jump middair. This only barely deviates from a standard jump, and is banned.
When the player is knocked airborne after taking damage, it is also possible to jump out of the hitstun.
Releasing a pole early by pressing A puts the player in a jumplike state.
Triangle jumps are parallel jumps between walls and are banned by technicality, for reasons explained in the video.
In power formation, when the power character is unable to move (i.e. after a combo), but the speed character can, it is possible to input a jump where only the speed/flying characters will jump, and the player character will remain stationary. This is banned because it circumvents the Triangle Jump technicality, as well as resets the ability to use Tornado (more info in the video). However, having the power or flying followers jump is okay, as no advantages exist for doing so.
Initiating flight in the flight formation.

Permitted actions that are similar to jumps:
Pressing A to release a lift ring/swinging vine. While the former does put the player in a jumplike state, it does not reset tornado or triangle jump (again, explained in video), and the jumpstate offers no meaningful advantages. I personally just thought it would be lame to keep getting softlocked on chinup bars with no way to let go.
Rail switching is also allowed, though I did scrutinize this one a lot. The reason for allowing it is that only sideways momentum is gained, and railswitching onto nothing puts the player in freefall, not a jumpstate. No actions can be inputted while in freefall. However, holding neutral on the control stick to jump off a railing is the same as a standard jump, and as such is not allowed.

All gameplay was recorded on the Dolphin Gamecube emulator. Save states were used to gather most of the footage.
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Music used:

Circuit Theme Mario and Sonic at the Sochi 2014 Olympic Winter Games
Bowser's Galaxy Generator Mario and Sonic at the Sochi 2014 Olympic Winter Games
Good Egg Galaxy Mario and Sonic at the Sochi 2014 Olympic Winter Games
Deltarune The Door
Mario and Luigi Bowser's Inside Story Tutorial Theme
Tokyo Daylight Persona 5
Sweatshop Persona 5
Break the Targets Super Smash Bros. Melee
Purple Comet Super Mario Galaxy
Casino Night Pinball Sonic Generations
Delightful Spekkio Chrono Trigger
Metallic Madness Zone Act 2 Sonic Mania
Riders Of The Light Bayonetta
Undertale An Ending
Danganronpa Class Trial Solar Edition
Map Music Donkey Kong Country
Fossil Falls Mario Odyssey
In the Halls of the Usurper Shovel Knight
The Trial Chrono Trigger
Danganronpa 2 Re_ Trial Underground
Meta Knight's Revenge Super Smash Bros. Brawl
Battlerock Galaxy theme Super Mario Galaxy
N Battle Pokemon Black 2 and White 2
Tera Raid Victory Pokemon Scarlet and Violet