I'm very curious to know as well. However, in the illustration, a whole lot of that water would be in low earth orbit, so the thought experiment gets complicated ;)

At first I thought perhaps you could use tsunami wave speed data for a very rough estimate. But that's wrong, because tsunami speed (roughly between 500 and 900 km/hr depending on ocean depth) is a measure of the wave energy propagating through the ocean, not a measure of the water's speed over ground.

Instead, perhaps one could start by using a model for the flow of water from a catastrophic dam breach. Hopefully someone more mathematically inclined than I will give it a go...

Last ice age ended: glaciers in Canada slowly melted, forming huge mile-high lakes within the rotting ice.

One spring day the rotting ice broke, the lakes surged free, travelled downhill as they must, ending in the gulf of mexico.

Took all summer, carved the Mississippi valley. According to the storey in the interpretive center near Pike's Peak.

Would there be temperature change as well?

Being high doesn't put you in orbit, it takes velocity relative to Earth to do that.

(Rockets going into orbit aren't just climbing, they're also building ground-speed. If there were an imaginary tower from ground to low-earth-orbit height, climbing it wouldn't put you in orbit - if you let go of something at the top of that tower, it would just fall.)

Unless the tower reaches to geosynchronous orbit (~36,000 km altitude). Then you've got a space elevator.

You do get some relative velocity due to the earth's rotation, it's just not enough to put you in orbit until you reach geosynchronous altitude (from your imaginary tower, not necessarily the imaginary sphere of water).

It's still not enough. At the equator, to do one revolution per day, you're doing ~1000mph. At 36,000km, because the circumference of the orbit is much longer than the circumference at ground level, to do one revolution per day, you need to be doing ~6900mph. So even if you get to geosynch, you still need to pick up ~5900mph sideways in linear velocity. As well as the energy it takes to get up there.

Somebody please make a physical simulation of this and animate it.

If someone does, please drop the blob over an existing ocean; I don't want all the trees washed away!

It includes the biological water that would include the water in trees as well. Well, unless you are saying the dead trees...