Can I tap Kaisa for Thousand-Tailed Watcher power cost?

No, you cannot tap Kai'Sa, Daughter of the Void to pay for costs associated with Thousand-Tailed Watcher.

According to her card text and the retrieved RiftJudge FAQs (specifically #5342, #2206, and #4346):

1. Kai'Sa's ability restriction: Kai'Sa's legend ability provides power that can only be used to pay for spells.
2. Not a spell: Thousand-Tailed Watcher is a unit card. Even its "When you play me" ability is a triggered ability of a unit, not a spell card.
3. Deflect costs: Additionally, per FAQ #8483 and #1048, Thousand-Tailed Watcher's "When you play me" ability does not target enemy units; it applies a blanket effect. Therefore, there is no "Deflect" cost to pay to begin with, and you do not need to use resources to satisfy any such cost.

In summary, Kai'Sa's power generation cannot be applied to unit costs, and there is no cost for Thousand-Tailed Watcher's ability that you could apply it to anyway.