fix(skills): keep watcher startup from marking chats stale

[danyaberezun]

Summary

• publish the watcher's synthetic startup invalidation as pathless and non-truncated, so live readers still refresh without falsely marking every chat's skills stale
• preserve conservative Skills staleness for real skill-path changes and genuinely truncated watcher batches
• document the refined wire semantics and add store, watcher, and browser regression coverage

User-visible behavior

• Before: opening a clean workspace could add the Skills reload dot after the watcher's delayed startup nudge, even though no skill changed
• After: watcher startup leaves the Skills indicator clean; a real skill file change still raises it and Reload still clears it per chat

Verification

• bun run check:deps
• bun run check:seams
• bun run lint (passes; reports the existing apps/website/src/styles.css specificity warning)
• bun run typecheck
• bun run test
• bunx playwright test e2e/skills-reload.live.spec.ts
• bun run e2e — 174 passed

[jetbrains-air]

Requesting changes — please address the blocking inline finding.

[jetbrains-air]

Requesting changes — please address the blocking inline finding.

[jetbrains-air]

Approved — ready to merge.

[jetbrains-air]

Approved — ready to merge.