If I use Temporal Breach a gear turned into a unit by Orianna’s legend ability, does it get replayed as a gear, as a unit gear, or does it stay banished?

It comes back as a plain Gear, not a unit gear — and because it lands at a battlefield as an unattached non-Unit Gear, it's Recalled to your Base in the next cleanup.

The banishment works fine (a unit gear is a unit, so it's a legal target), but the card changes zones to a non-board zone, which makes it a new object and clears all applied layer alterations — including Orianna's type change (Rule 124). At that point it's just its printed Gear card, and the "until you choose another gear" effect is gone; Orianna would have to choose it again at the start of a later Main Phase. Note it is not stuck in banishment: Temporal Breach specifies the location, which is the "unless an effect specifies otherwise" carve-out for playing Gear somewhere other than Base (Rules 149.2, 152.2) — so the replay is legal, it just enters as Gear and gets recalled as a corrective action (Rule 457.1).

Net effect: you get the card back as a Base Gear (ready), it isn't a unit, and no Contested/Showdown results from the replay. If it was breached while at your Base, it simply re-enters at Base with no recall step needed.