Callr

The watch goes back to the clock during a game.
Turn on Track as workout in Callr on the watch and allow Health access. Or set Settings > General > Return to Clock > Callr to 1 hour.

Why does the game start at 0-0-2?
In doubles with traditional scoring, the team that serves first gets only one server in its first turn, so the first server is called server 2 (USA Pickleball rule 5.B). After the first side out, both partners serve in every turn.

How does Callr know where each player stands?
By the official rule: the player who started the game on the right is on the right when the team's score is even, and on the left when it is odd. If you set the wrong starting positions, tap Swap before the first rally.

The voice is too quiet or I don't want it.
Callr speaks through the media volume, even with the ringer on silent. Tap the speaker button during a game to turn it off.

I tapped the wrong team.
Tap Undo (the curved arrow). You can undo any number of rallies, even after the game ended.

Do the iPhone and the watch sync?
Not yet. Each one keeps its own game.