perf(skills): full multi-root recursive skill rescan on every prompt build, load_skill call, and /skills command

[Hmbown]

Problem

Skill discovery re-walks up to ~10 roots recursively (depth 8, with per-dir fs::canonicalize) on every prompt construction, every load_skill tool call, and every /skills invocation — for data that changes rarely.

Evidence

• crates/tui/src/prompts.rs:1240-1254 — the ## Skills system-prompt block re-runs discovery from disk on each prompt build.
• crates/tui/src/skills/mod.rs:160-283 — the walk (canonicalize per directory at :280); roots list at :550-584 — note the workspace-root skills/ candidate (:558) means any repo with an unrelated top-level skills/ tree gets an 8-level recursive walk every turn.
• crates/tui/src/tools/skill.rs:98-104 and skills.rs:23-29 repeat the walk per call.

Impact

Per-turn latency proportional to workspace layout — worst on big monorepos with a coincidental skills/ directory or large ~/.agents/skills libraries.

Proposed approach

Cache the merged SkillRegistry keyed by (dir list, per-root mtime): stat the roots and re-walk only when an mtime changed; invalidate explicitly on /skill install|uninstall|update (hooks already exist: refresh_skill_cache, app.rs:2882-2889).

Acceptance criteria

• Subsequent prompt builds in an unchanged workspace do zero recursive walks (verifiable via a discovery counter in tests); adding/removing a SKILL.md is still picked up on the next turn; load_skill uses the same cache.

[Hmbown]

Verified complete in v0.9.3 (c98648b1c0f2a82ddaf7d2d82f8212e065db9b65). The cache, invalidation, explicit clear, shared load_skill path, and same-timestamp edit handling shipped in 8dda5bae9834, bb569562dcfe, bbc66e62dd79, and 5667d6e0c2f0. The named cache acceptance tests passed in the v0.9.3 release train (PR #4993). Closing as completed.