She does have one very grand staircase that is wide and straight and shallow.

Does it have banisters with a nice drop to the side?

Yup.

He steps into a side room to change.

He comes back out at a run, flickers of yellow and white showing under the brown and orange, and dashes all the way up to the top of staircase, spins and just holds a pose for a moment, arms wide.

Tarinda applauds.

He walks down a step, and another, and two at a time, three, five, eight, bands of deep blue and bright cyan, nine, who's counting, there's the bottom, thump perfect landing without another step taken.

"Neato!" Clap clap clap.

“Next, upper body safety chec—” He falls down backwards in what ordinarily would be a moderately uncomfortable manner on a stone floor.

“Check!” Thumbs up!

Giggle.

He goes a few steps up, grabs the railing with both hands, checks it for sturdiness, and swings over it to drop to the floor beside. The landing isn't so great without enough height to work with.

Then again higher, and neater (and blue and some green).

“Working as designed!”

"Very cool indeed. You gonna go down the mountain too or are you getting tired?"

“I'll go down gently and call it a practice run.”

"Enjoy."

Presumably if he heads in the downstairs direction of the grand staircase that is likely to lead further Out and Down.

Yup. The mountain is gorgeous.

He may have more trouble than he was anticipating not stomping on any gorgeousness on the way down.

He climbs a nearby rock to get a better view and plans a route comfortably separate from the patches of landscaping and sculpture, but not so far away that he won't get to see them.

And he jumps, down, red-orange and blue-cyan and red-orange again to any observers that might happen to be present, making his way to the base of the mountain.

It's a pretty jumpable mountain!

Now he is at the bottom of it.

Dear helpful information technology, how does he get “home” from here?

If he wants to go to sleep where he woke up, thataway. Zoomer?

Might as well. Are they, like, sitting around, or does one fly itself over just for him, or …?

Once he orders one, a zoomer zooms out of some hiding place on the mountain and presents itself.

Cool. He will steer himself, thanks, just point him in the proper direction.

And in the evening light he flies to his residence for the time being, wearing the colors of a sunset.

(Oops, he left his one and only set of regular clothes at Tarinda's castle, didn't he. This is probably a trivial problem.)

If he'd like to order some clothes they can be delivered to his room at the facility where sleepers wake.

— actually it might as well be bedtime, he is going to sleep, are pajamas a thing? Or is all Future Clothing™ entirely comfortable and oil-sweat-and-rumple-proof?

Pajamas can be a thing if he desires pajamas! Not all future clothing is made of any specific futuristic material.