How much of the celestial sphere can an Earth observer see at one time?

Approximately 50% like anywhere else on the planet. The difference at the poles is that it is the same 50% all night and all year.

The reason it is approximate is that:

1/ If you are high up you will see a little more than 50% due to the curve of the Earth.

2/ If the land around you has hills they will block some of your view reducing the percentage a little.