If I play hostile takeover to take my opponents unit on my turn and it gets returned to them at the end of turn, does it become ready?

Yes — the unit returns ready.

Hostile Takeover readies the unit when you take control, and Recalls don't change a permanent's state (Rule 458) — so it goes back to your opponent's Base in whatever state it's in at end of turn, which is ready unless something exhausted it while you controlled it. The control handover at end of turn also has no effect on its ready/exhausted state.

One edge: if you (or a spell) exhausted the unit during your turn, it will return exhausted instead. And since your opponent's Awakening Phase has already passed, it'll stay that way until their next turn starts.