Can you play Star-Crossed to someone playing a Thousand-Tailed Watcher?

Yes, you can play Star-Crossed in response to an opponent playing Thousand-Tailed Watcher.

Why this works

1. Timing: When your opponent plays Thousand-Tailed Watcher, it enters the battlefield and its "When you play me" ability is placed on the chain. Because this is a triggered ability, it uses the chain and can be reacted to (as confirmed by RiftJudge FAQ #6628).
2. Reaction Permission: Cards with the [Reaction] keyword can be played during Closed States (when the chain is not empty), per Rule 813.1.c.1.
3. Targeting: Star-Crossed requires both a friendly unit and an enemy unit to be played (RiftJudge FAQ #9452). As long as you have a friendly unit and the Thousand-Tailed Watcher (or another enemy unit) is on the board, you have valid targets.

Chain and Resolution

Riftbound uses a Last-In, First-Out (LIFO) resolution order, meaning the most recently added item resolves first (Rule 340.1).

Sequence:

1. Opponent plays Thousand-Tailed Watcher: The unit enters play, and its "When you play me" ability is added to the chain.
2. You play Star-Crossed: You add Star-Crossed to the top of the chain in response to the Watcher's ability.
3. Resolution:
   • Star-Crossed resolves first: It returns your chosen friendly unit and the enemy Thousand-Tailed Watcher to their owners' hands.
   • Watcher's ability resolves second: Even though the Thousand-Tailed Watcher is no longer on the board, its ability was already on the chain. According to RiftJudge FAQ #3100, abilities do not "fizzle" just because the source unit left the board; the ability will resolve, though it may have no effect if it no longer has valid targets or if the game state has changed such that the instructions cannot be followed (Rule 359.3.e.6).

Note: I could not fully verify this ruling against the retrieved rules.