Move host skill prompt injection into the skills extension (#37503)

## What changed

- Add `HostSkillsSnapshot::load_skill_prompts` so the skills extension owns reading and rendering selected host skills.
- Keep explicit invocation telemetry, unreadable-skill warnings, plugin prompt ordering, and suppression of host prompts superseded by provider prompts.
- Remove the legacy prompt injection and fragment implementation from `codex-core-skills`.

## Testing

- Cover prompt truncation without an installed skills extension, skill/plugin ordering, selective provider supersession, unreadable skills, and contextual fragment detection.

GitOrigin-RevId: 9c8b84ad54b90d174abc287ab49cc5a231e9e1aa

codex-rs/core/src/context/contextual_user_message.rs

@@ -9,7 +9,6 @@ use super::LegacyApplyPatchExecCommandWarning;
 use super::LegacyModelMismatchWarning;
 use super::LegacyUnifiedExecProcessLimitWarning;
 use super::RecommendedPluginsInstructions;
-use super::SkillInstructions;
 use super::SubagentNotification;
 use super::TurnAborted;
 use super::UserInstructions;
@@ -20,7 +19,7 @@ const CONTEXTUAL_USER_FRAGMENT_MATCHERS: &[fn(&str) -> bool] = &[
     UserInstructions::matches_text,
     EnvironmentsState::matches_text,
     AdditionalContextUserFragment::matches_text,
-    SkillInstructions::matches_text,
+    codex_skills_extension::is_skill_prompt_fragment,
     UserShellCommand::matches_text,
     TurnAborted::matches_text,
     SubagentNotification::matches_text,

codex-rs/core/src/context/contextual_user_message_tests.rs

@@ -15,6 +15,18 @@ fn detects_environment_context_fragment() {
     }));
 }
 
+#[test]
+fn detects_skill_instructions_fragment_case_insensitively() {
+    for text in [
+        "<skill>\n<name>demo</name>\n</skill>",
+        "  <SKILL>\n<name>demo</name>\n</SKILL>  ",
+    ] {
+        assert!(is_contextual_user_fragment(&ContentItem::InputText {
+            text: text.to_string(),
+        }));
+    }
+}
+
 #[test]
 fn detects_agents_instructions_fragment() {
     for text in [

codex-rs/core/src/context/mod.rs

@@ -43,7 +43,6 @@ pub(crate) use available_plugins_instructions::AvailablePluginsInstructions;
 pub(crate) use codex_context_fragments::AdditionalContextDeveloperFragment;
 pub(crate) use codex_context_fragments::AdditionalContextUserFragment;
 pub use codex_context_fragments::ContextualUserFragment;
-pub(crate) use codex_core_skills::SkillInstructions;
 pub(crate) use contextual_user_message::is_contextual_user_fragment;
 pub(crate) use contextual_user_message::parse_visible_hook_prompt_message;
 pub(crate) use current_time_reminder::CurrentTimeReminder;