[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/tools/handlers/shell.rs

@@ -52,7 +52,6 @@ struct RunExecLikeArgs {
     turn: Arc<TurnContext>,
     tracker: crate::tools::context::SharedTurnDiffTracker,
     call_id: String,
-    freeform: bool,
     shell_runtime_backend: ShellRuntimeBackend,
 }
 
@@ -68,7 +67,6 @@ async fn run_exec_like(args: RunExecLikeArgs) -> Result<FunctionToolOutput, Func
         turn,
         tracker,
         call_id,
-        freeform,
         shell_runtime_backend,
     } = args;
 
@@ -162,12 +160,7 @@ async fn run_exec_like(args: RunExecLikeArgs) -> Result<FunctionToolOutput, Func
     }
 
     let source = ExecCommandSource::Agent;
-    let emitter = ToolEmitter::shell(
-        exec_params.command.clone(),
-        exec_params.cwd.clone(),
-        source,
-        freeform,
-    );
+    let emitter = ToolEmitter::shell(exec_params.command.clone(), exec_params.cwd.clone(), source);
     let event_ctx = ToolEventCtx::new(
         session.as_ref(),
         turn.as_ref(),

codex-rs/core/src/tools/handlers/shell/shell_command.rs

@@ -197,7 +197,6 @@ impl ToolExecutor<ToolInvocation> for ShellCommandHandler {
             turn,
             tracker,
             call_id,
-            freeform: true,
             shell_runtime_backend: self.shell_runtime_backend(),
         })
         .await