All players can see the current keystone given by a player who uses Omnistone.

The indicator will appear just next to your HP bar, and it appears the same for both allies and enemies of the Omnistone user.

Here's a screenshot of how it looks on an enemy champion:

Nothing really different than if I was looking at myself or an ally's HP bar, provided they were using Omnistone too.

All players can see the keystone that's currently ready to be used by a player who uses Omnistone.

The indicator will appear just next to the Omnistone user's HP bar, and it appears the same for both allies and enemies of the Omnistone user.

Here's a screenshot of how it looks on an enemy champion:

Nothing changes in the visibility of this indicator. It doesn't matter if you're the user, an ally of the user, or an enemy of the user.