[Androzani84]

Here we are, twice in one day (from my perspective):

Ridewatch Playlist - I can’t believe it’s not Magiranger mix

“With the magical rings, it’s showtime. The jewelled Rider is… Wizard”

And we’re giving him his theme song this time, Life is SHOW TIME

“4 elements become 1. Wizard All Dragon”

Surprisingly, they actually made a song for this form, Alteration

“The magical stone that shines forever. The seriously amazing magician, Wizard Infinity Style”

And I’m being boring with the descriptions this time, because I can’t think of what to say. Here’s Missing Piece

“Fighting with the power of beasts, the golden lion Rider is Beast”

First time I’d heard of this song, BEASTBITE

“The time has come to awaken the blue lion, Beast Hyper”

And now, the list of the unreleased (no winners this time)

Kamen Rider Wizard (Water Style)
Kamen Rider Wizard (Hurricane Style)
Kamen Rider Wizard (Land Style)
Kamen Rider Wizard (Flame Dragon)
Kamen Rider Wizard (Water Dragon)
Kamen Rider Wizard (Hurricane Dragon)
Kamen Rider Wizard (Land Dragon)
Kamen Rider Wizard (Special Rush)
Kamen Rider Wizard (Infinity Dragon)
Kamen Rider Wizard (Infinity Dragon Gold)
White Mage (Wiseman)
Kamen Rider Sorcerer
Kamen Rider Mage (Amber)
Kamen Rider Mage (Blue)
Kamen Rider Mage (Green)

As for the compare and contrast, you’ve already pointed out how Hayase falls into despair easily, but I’ll also point out that he’s misusing his magic for personal gain, contrasting with Haruto using it to bring hope to people (and also, his “belt voices” exclude the “please” at the end). His monster form is basically “What if Dragon managed to send Haruto into despair successfully and taken over his body”, with some cracks on his face reminiscent of a Gate.

As for the episode, the show about Gates gets homages with focus on Geiz. Given that Toei studio has been blown up and the screenwriters have cut Sougo out, someone has to take over.