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/protocol/src/protocol.rs

@@ -193,6 +193,10 @@ pub enum Op {
         /// When empty, the session default working directory is used.
         #[serde(default, skip_serializing_if = "Vec::is_empty")]
         cwds: Vec<PathBuf>,
+
+        /// When true, recompute skills even if a cached result exists.
+        #[serde(default, skip_serializing_if = "std::ops::Not::not")]
+        force_reload: bool,
     },
 
     /// Request the agent to summarize the current conversation context.
@@ -609,6 +613,9 @@ pub enum EventMsg {
     /// List of skills available to the agent.
     ListSkillsResponse(ListSkillsResponseEvent),
 
+    /// Notification that skill data may have been updated and clients may want to reload.
+    SkillsUpdateAvailable,
+
     PlanUpdate(UpdatePlanArgs),
 
     TurnAborted(TurnAbortedEvent),
@@ -1683,6 +1690,7 @@ pub struct ListSkillsResponseEvent {
 pub enum SkillScope {
     User,
     Repo,
+    Public,
 }
 
 #[derive(Debug, Clone, Deserialize, Serialize, JsonSchema, TS)]