The next half-pipe is in Tallon Overworld so head there. The hint system will probably be pointing to it already.
Go to Tallon Canyon and locate the half-pipe near the door to Transport Tunnel A. Do a half-pipe jump to reach the ledge on one side. The ledge is higher than the other ones you've encountered so far, so this will be a real test of your half-pipe skills.
Cross the bridge to a sandstone wall, bomb it open and follow the tunnel, bombing more walls as you come to them. Drop off a ledge to find a door at the end of the passage.
There are some Zoomers patrolling this passage. Drop down the ledges to the next door.
If you're having Déjà vu now it's because this is the second time you've had to take a roundabout route to get to an inaccessible part of a room where you've already been. Is this going to be the last time the game pulls this trick?
Hop along the ledges to another door on the left.
Drop down the ledge and find the Space Jump Boots inside a golden beam of light. (This isn't Mario so looking into the light doesn't magically transport you anywhere.)
The boots allow you to do a double jump; jump and jump again in mid-air to get additional height or distance. This makes getting around in the areas you've explored so far much easier. On the other hand getting around in future areas will often require this move so your platforming skills will still be in demand.
You will, of course, have to use the double jump to escape from this room. Do so and since you're so close to the ship you might as well save there.
Expansions (Chozo Ruins)
Though the double jump is useful, there is only one expansion it allows you to get now. It's a bit out of your way so you may want to postpone getting it until you're in the area anyway, when you're on the way to get the Ice Beam for example.
Get to the Gathering Hall as before. Note that between having the double jump and the fact that the water is no longer toxic, you can now get around the Chozo Ruins fairly quickly. Get to the top of the room; again the double jump allows you to skip most of the ledges you needed before. Hop onto one of the two small red cylinders on either side of the door. Double jump from there onto a ledge over the door. Switch to Morph Ball and drop a bomb to clear the wall there, then grab the Missile Expansion behind it.
There are two other places where the double jump opens some new exploration, but neither of them result in anything useful now so we'll just mention them now.
The first is in the Magmoor Caverns Monitor Station. You may notice that next to the bridge leading to Transport Tunnel A is a small platform. You can double jump to it and from there to another bridge above the one you were just on.
The second is in Phendrana Drifts, in Ice Ruins West. You can use the double jump to get to rooftop level, but you'll need the Wave Beam to go on from there. The Wave Beam is the next upgrade so you'll be returning to Ice Ruins West soon enough.