[codex] Remove legacy shell output formatting paths (#22706)

## Why

The client and tool pipeline still carried compatibility code for legacy
structured shell output. Current shell and apply_patch responses are
already plain text for model consumption, so keeping a
JSON-serialization path plus shell-item rewrite logic makes the request
formatter and tests preserve a format we do not need anymore.

## What Changed

- Removed the client-side shell output rewrite from
`core/src/client_common.rs`.
- Removed the structured exec-output formatter and the shell `freeform`
switch so tool emitters use one model-facing formatter.
- Collapsed apply_patch/shell serialization tests around the remaining
plain-text output expectations and removed duplicate one-variant
parameterized cases.
- Kept the `ApplyPatchModelOutput::ShellCommandViaHeredoc` compatibility
input shape, but no longer treats it as a separate output-format mode.

## Validation

- `cargo test -p codex-core client_common`
- `cargo test -p codex-core shell_serialization`
- `cargo test -p codex-core apply_patch_cli`
- `just fix -p codex-core`

## Documentation

No external Codex documentation update is needed.

codex-rs/core/src/client_common_tests.rs

@@ -3,7 +3,6 @@ use codex_api::ResponsesApiRequest;
 use codex_api::TextControls;
 use codex_api::create_text_param_for_request;
 use codex_protocol::config_types::ServiceTier;
-use codex_protocol::models::FunctionCallOutputPayload;
 use pretty_assertions::assert_eq;
 
 use super::*;
@@ -166,65 +165,3 @@ fn serializes_flex_service_tier_when_set() {
         Some("flex")
     );
 }
-
-#[test]
-fn reserializes_shell_outputs_for_function_and_custom_tool_calls() {
-    let raw_output = r#"{"output":"hello","metadata":{"exit_code":0,"duration_seconds":0.5}}"#;
-    let expected_output = "Exit code: 0\nWall time: 0.5 seconds\nOutput:\nhello";
-    let mut items = vec![
-        ResponseItem::FunctionCall {
-            id: None,
-            name: "shell".to_string(),
-            namespace: None,
-            arguments: "{}".to_string(),
-            call_id: "call-1".to_string(),
-        },
-        ResponseItem::FunctionCallOutput {
-            call_id: "call-1".to_string(),
-            output: FunctionCallOutputPayload::from_text(raw_output.to_string()),
-        },
-        ResponseItem::CustomToolCall {
-            id: None,
-            status: None,
-            call_id: "call-2".to_string(),
-            name: "apply_patch".to_string(),
-            input: "*** Begin Patch".to_string(),
-        },
-        ResponseItem::CustomToolCallOutput {
-            call_id: "call-2".to_string(),
-            name: None,
-            output: FunctionCallOutputPayload::from_text(raw_output.to_string()),
-        },
-    ];
-
-    reserialize_shell_outputs(&mut items);
-
-    assert_eq!(
-        items,
-        vec![
-            ResponseItem::FunctionCall {
-                id: None,
-                name: "shell".to_string(),
-                namespace: None,
-                arguments: "{}".to_string(),
-                call_id: "call-1".to_string(),
-            },
-            ResponseItem::FunctionCallOutput {
-                call_id: "call-1".to_string(),
-                output: FunctionCallOutputPayload::from_text(expected_output.to_string()),
-            },
-            ResponseItem::CustomToolCall {
-                id: None,
-                status: None,
-                call_id: "call-2".to_string(),
-                name: "apply_patch".to_string(),
-                input: "*** Begin Patch".to_string(),
-            },
-            ResponseItem::CustomToolCallOutput {
-                call_id: "call-2".to_string(),
-                name: None,
-                output: FunctionCallOutputPayload::from_text(expected_output.to_string()),
-            },
-        ]
-    );
-}