Remove the unused legacy remote compaction implementation (#44273)

## Why

Remote compaction already uses the normal Responses API, leaving the legacy `/responses/compact` runner unused.

## What changed

- Remove the legacy runner, endpoint client, request types, analytics variant, and obsolete test helpers and snapshots.
- Move tool-output trimming and its metadata tests into `compact_remote_history` for reuse by remote compaction v2.
- Consolidate retained-history filtering in the v2 implementation and remove redundant `RemoteCompactionV2` settings from tests.

## Testing

Extend the retained-history unit test to explicitly check that hook prompts survive compaction.

GitOrigin-RevId: 999bb1391aa22c3c281d6a96f98817d6c9e46ed9

codex-rs/codex-api/src/common.rs

@@ -43,28 +43,6 @@ impl From<CyberAccessProgram> for AccessPrograms {
     }
 }
 
-/// Canonical input payload for the compaction endpoint.
-#[derive(Debug, Clone, Serialize)]
-pub struct CompactionInput<'a> {
-    pub model: &'a str,
-    pub input: &'a [ResponseItem],
-    #[serde(skip_serializing_if = "str::is_empty")]
-    pub instructions: &'a str,
-    #[serde(skip_serializing_if = "Option::is_none")]
-    pub tools: Option<ResponsesApiTools>,
-    pub parallel_tool_calls: bool,
-    #[serde(skip_serializing_if = "Option::is_none")]
-    pub reasoning: Option<Reasoning>,
-    #[serde(skip_serializing_if = "Option::is_none")]
-    pub service_tier: Option<&'a str>,
-    #[serde(skip_serializing_if = "Option::is_none")]
-    pub prompt_cache_key: Option<&'a str>,
-    #[serde(skip_serializing_if = "Option::is_none")]
-    pub text: Option<TextControls>,
-    #[serde(skip_serializing_if = "Option::is_none")]
-    pub access_programs: Option<AccessPrograms>,
-}
-
 /// Canonical input payload for the memory summarize endpoint.
 #[derive(Debug, Clone, Serialize)]
 pub struct MemorySummarizeInput {