If a soldier that has been moved with Azir Sovereign that goes to the battlefield ready, is recalled to base because it does not conquer but it also doesn't die, does it go to base ready?

Yes — the soldier returns to base ready.

Azir's ability moves tokens via an effect, not a Standard Move, so there is no exhaust cost — they arrive at the battlefield ready. If combat resolves with defenders still present, Combat Cleanup recalls the attackers (Rule 461.1.a.2). Recalls do not change a unit's state (Rule 453), so the soldier is recalled in whatever state it's in — still ready.