If I use Baited Hook on my last unit at a battlefield, can I still play the unit from Baited Hook to that battlefield?

Yes, you can play the unit to the battlefield where the original unit was killed.

According to RiftJudge FAQ #8752 (which addresses this specific interaction), battlefields only become uncontrolled when they are empty during an Open State. Because the game enters a Closed State while Baited Hook is resolving on the chain, control of the battlefield is locked throughout the entire process, including the moment it is temporarily unoccupied.

Sequence of Events:

1. Activation: You pay the costs (1 Energy, 1 Order Power, and Exhaust the Gear) and declare a target friendly unit at the battlefield.
2. Resolution Starts (Closed State): The ability begins to resolve. The game is now in a Closed State, meaning your control of the battlefield is locked.
3. Kill Effect: The targeted friendly unit is killed and sent to the trash.
4. Look & Select: You look at the top 5 cards of your Main Deck and choose a unit with appropriate Might.
5. Placement: You play the chosen unit to the now-vacant battlefield.
6. Resolution Ends: The chain finishes resolving, and the game returns to an Open State. Since there is now a unit present at the battlefield, you retain control.

Note: This ruling is based on the mechanics of the Closed State and Rule 187.4.c, as clarified in the Riftbound rules update.