Omit service_tier from remote /responses/compact requests under API auth (#21676)

## Summary

API-key-auth remote compaction requests should not inherit
`service_tier` from normal `/responses` turns. This path needs to match
API auth expectations, while ChatGPT-auth remote compaction should keep
reusing the shared request fields that still apply there.

This change keeps the decision inline in
`codex-rs/core/src/compact_remote.rs` only. Under API key auth, the
classic remote `/responses/compact` path now omits `service_tier`; under
ChatGPT auth, it keeps reusing the configured tier.
`codex-rs/core/src/compact_remote_v2.rs` is unchanged. The remote
compaction parity coverage and snapshots were updated to assert the
API-key omission and preserve the ChatGPT-auth behavior.

## Testing

- Updated remote compaction parity coverage in
`codex-rs/core/tests/suite/compact_remote.rs` and the corresponding
snapshots.

codex-rs/core/tests/suite/compact_remote.rs

@@ -664,15 +664,16 @@ async fn assert_remote_manual_compact_request_parity(
 }
 
 #[tokio::test(flavor = "multi_thread", worker_threads = 2)]
-async fn remote_manual_compact_api_auth_reuses_prompt_cache_key() -> Result<()> {
+async fn remote_manual_compact_api_auth_omits_service_tier_and_reuses_prompt_cache_key()
+-> Result<()> {
     skip_if_no_network!(Ok(()));
 
     assert_remote_manual_compact_request_parity(
         CodexAuth::from_api_key("dummy"),
         Some(ServiceTier::Fast),
-        Some("priority"),
+        /*expected_service_tier*/ None,
         "remote_manual_compact_api_auth_prompt_cache_key_request_diff",
-        "After five varied API-key-auth turns, remote manual compaction reuses the normal responses service_tier and prompt_cache_key while omitting responses-only fields.",
+        "After five varied API-key-auth turns, remote manual compaction omits service_tier, reuses prompt_cache_key, and still omits responses-only fields.",
     )
     .await?;
 
@@ -689,7 +690,7 @@ async fn remote_manual_compact_chatgpt_auth_reuses_service_tier_and_prompt_cache
         Some(ServiceTier::Fast),
         Some("priority"),
         "remote_manual_compact_chatgpt_auth_service_tier_prompt_cache_key_request_diff",
-        "After five varied ChatGPT-auth turns, remote manual compaction reuses the normal responses service_tier and prompt_cache_key while omitting responses-only fields.",
+        "After five varied ChatGPT-auth turns, remote manual compaction reuses service_tier and prompt_cache_key while omitting responses-only fields.",
     )
     .await?;
 

codex-rs/core/tests/suite/snapshots/all__suite__compact_remote__remote_manual_compact_api_auth_prompt_cache_key_request_diff.snap

@@ -2,7 +2,7 @@
 source: core/tests/suite/compact_remote.rs
 expression: "context_snapshot::format_request_body_diff_snapshot(scenario,\n\"Last Normal /responses Request\", &normal_request,\n\"Remote /responses/compact Request\", &compact_request,\n&ContextSnapshotOptions::default(),)"
 ---
-Scenario: After five varied API-key-auth turns, remote manual compaction reuses the normal responses service_tier and prompt_cache_key while omitting responses-only fields.
+Scenario: After five varied API-key-auth turns, remote manual compaction omits service_tier, reuses prompt_cache_key, and still omits responses-only fields.
 
 --- Last Normal /responses Request
 +++ Remote /responses/compact Request
@@ -38,6 +38,7 @@ Scenario: After five varied API-key-auth turns, remote manual compaction reuses
 +      ],
 +      "role": "assistant",
 +      "type": "message"
+-  "service_tier": "priority",
 -  "store": false,
 -  "stream": true,
 -  "tool_choice": "auto",

codex-rs/core/tests/suite/snapshots/all__suite__compact_remote__remote_manual_compact_chatgpt_auth_service_tier_prompt_cache_key_request_diff.snap

@@ -2,7 +2,7 @@
 source: core/tests/suite/compact_remote.rs
 expression: "context_snapshot::format_request_body_diff_snapshot(scenario,\n\"Last Normal /responses Request\", &normal_request,\n\"Remote /responses/compact Request\", &compact_request,\n&ContextSnapshotOptions::default(),)"
 ---
-Scenario: After five varied ChatGPT-auth turns, remote manual compaction reuses the normal responses service_tier and prompt_cache_key while omitting responses-only fields.
+Scenario: After five varied ChatGPT-auth turns, remote manual compaction reuses service_tier and prompt_cache_key while omitting responses-only fields.
 
 --- Last Normal /responses Request
 +++ Remote /responses/compact Request