Does Blue Sentinel make me exhaust an extra rune or is it floating energy?

Blue Sentinel does not cause you to exhaust an extra rune.

According to its card text, when Blue Sentinel holds a battlefield, its ability triggers: "When I hold, [Add] [A] at the start of your next Main Phase."

This ability adds 1 Power of any domain (Universal Power) to your Rune Pool at the start of your next Main Phase. It does not require you to exhaust any runes to generate this resource; it is an effect that automatically adds the resource to your pool at the specified time.