Add public skills + improve repo skill discovery and error UX (#8098)

1. Adds SkillScope::Public end-to-end (core + protocol) and loads skills
from the public cache directory
2. Improves repo skill discovery by searching upward for the nearest
.codex/skills within a git repo
3. Deduplicates skills by name with deterministic ordering to avoid
duplicates across sources
4. Fixes garbled “Skill errors” overlay rendering by preventing pending
history lines from being injected during the modal
5. Updates the project docs “Skills” intro wording to avoid hardcoded
paths

codex-rs/mcp-server/src/codex_tool_runner.rs

@@ -304,6 +304,7 @@ async fn run_codex_tool_session_inner(
                     | EventMsg::AgentMessageContentDelta(_)
                     | EventMsg::ReasoningContentDelta(_)
                     | EventMsg::ReasoningRawContentDelta(_)
+                    | EventMsg::SkillsUpdateAvailable
                     | EventMsg::UndoStarted(_)
                     | EventMsg::UndoCompleted(_)
                     | EventMsg::ExitedReviewMode(_)