Can I activate a hidden temporal breach to play a brynhir or any other unit on another battlefield or base?

No. A Hidden Temporal Breach can only target a unit at the battlefield where it was hidden — it cannot reach a unit at another battlefield or at base.

Temporal Breach reads "Banish a unit," with no location restriction, so the general Hidden targeting rule applies: its target must be chosen from the battlefield associated with the facedown zone (Rule 811.1.d.2). The "plays it to the same location" clause is just a linked instruction that follows the unit wherever it was — it does not create the kind of impossible-target exception that cards like Tideturner have.

So the Brynhir play works only if Brynhir is at that same battlefield: banish her, she replays to the same location ignoring cost, and her "When you play me" trigger fires again. If she's anywhere else, you'd need to play Temporal Breach normally from hand, not from Hidden.