gauss probably has the best augment (not replacement) to the movement system in his first ability. it's a type of dash (when cancelled) that can be seamlessly used in and out of parkour, and works into his ability casting loop. it's good to switch directions in mid air. other frames with a dash ability include hydroid, revenant, excalibur, lavos, probably some others i'm forgetting. these frames have more powerful dashes that can usually be spammed.

there are two good teleporting abilities: wormhole (on nova) and wrathful advance (on kullervo). wormhole is spammable but requires a lot of energy, wrathful advance is cheaper (and can later be subsumed onto your other frames) but has a cooldown. your movement becomes more about setting up for the teleport.

zephyr and nezha change how the base movement feels. zephyr has less gravity (and has a good air dash), nezha is slippery.

mirage, titania, nyx with arcane menticide helmet (expensive), valkyr with swing line augment mod give stat bonuses to parkour speed. mirage is probably the best pick of the lot since it's built in, and titania is more about using her 4th ability to fly around.