[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.rs

@@ -2,13 +2,10 @@ pub use codex_api::ResponseEvent;
 use codex_config::types::Personality;
 use codex_protocol::error::Result;
 use codex_protocol::models::BaseInstructions;
-use codex_protocol::models::FunctionCallOutputBody;
 use codex_protocol::models::ResponseItem;
 use codex_tools::ToolSpec;
 use futures::Stream;
-use serde::Deserialize;
 use serde_json::Value;
-use std::collections::HashSet;
 use std::pin::Pin;
 use std::task::Context;
 use std::task::Poll;
@@ -64,116 +61,10 @@ impl Default for Prompt {
 
 impl Prompt {
     pub(crate) fn get_formatted_input(&self) -> Vec<ResponseItem> {
-        let mut input = self.input.clone();
-
-        // when using the *Freeform* apply_patch tool specifically, tool outputs
-        // should be structured text, not json. Do NOT reserialize when using
-        // the Function tool - note that this differs from the check above for
-        // instructions. We declare the result as a named variable for clarity.
-        let is_freeform_apply_patch_tool_present = self.tools.iter().any(|tool| match tool {
-            ToolSpec::Freeform(f) => f.name == "apply_patch",
-            _ => false,
-        });
-        if is_freeform_apply_patch_tool_present {
-            reserialize_shell_outputs(&mut input);
-        }
-
-        input
+        self.input.clone()
     }
 }
 
-fn reserialize_shell_outputs(items: &mut [ResponseItem]) {
-    let mut shell_call_ids: HashSet<String> = HashSet::new();
-
-    items.iter_mut().for_each(|item| match item {
-        ResponseItem::LocalShellCall { call_id, id, .. } => {
-            if let Some(identifier) = call_id.clone().or_else(|| id.clone()) {
-                shell_call_ids.insert(identifier);
-            }
-        }
-        ResponseItem::CustomToolCall {
-            id: _,
-            status: _,
-            call_id,
-            name,
-            input: _,
-        } => {
-            if name == "apply_patch" {
-                shell_call_ids.insert(call_id.clone());
-            }
-        }
-        ResponseItem::FunctionCall { name, call_id, .. }
-            if is_shell_tool_name(name) || name == "apply_patch" =>
-        {
-            shell_call_ids.insert(call_id.clone());
-        }
-        ResponseItem::FunctionCallOutput {
-            call_id, output, ..
-        }
-        | ResponseItem::CustomToolCallOutput {
-            call_id, output, ..
-        } => {
-            if shell_call_ids.remove(call_id)
-                && let Some(structured) = output
-                    .text_content()
-                    .and_then(parse_structured_shell_output)
-            {
-                output.body = FunctionCallOutputBody::Text(structured);
-            }
-        }
-        _ => {}
-    })
-}
-
-fn is_shell_tool_name(name: &str) -> bool {
-    name == "shell"
-}
-
-#[derive(Deserialize)]
-struct ExecOutputJson {
-    output: String,
-    metadata: ExecOutputMetadataJson,
-}
-
-#[derive(Deserialize)]
-struct ExecOutputMetadataJson {
-    exit_code: i32,
-    duration_seconds: f32,
-}
-
-fn parse_structured_shell_output(raw: &str) -> Option<String> {
-    let parsed: ExecOutputJson = serde_json::from_str(raw).ok()?;
-    Some(build_structured_output(&parsed))
-}
-
-fn build_structured_output(parsed: &ExecOutputJson) -> String {
-    let mut sections = Vec::new();
-    sections.push(format!("Exit code: {}", parsed.metadata.exit_code));
-    sections.push(format!(
-        "Wall time: {} seconds",
-        parsed.metadata.duration_seconds
-    ));
-
-    let mut output = parsed.output.clone();
-    if let Some((stripped, total_lines)) = strip_total_output_header(&parsed.output) {
-        sections.push(format!("Total output lines: {total_lines}"));
-        output = stripped.to_string();
-    }
-
-    sections.push("Output:".to_string());
-    sections.push(output);
-
-    sections.join("\n")
-}
-
-fn strip_total_output_header(output: &str) -> Option<(&str, u32)> {
-    let after_prefix = output.strip_prefix("Total output lines: ")?;
-    let (total_segment, remainder) = after_prefix.split_once('\n')?;
-    let total_lines = total_segment.parse::<u32>().ok()?;
-    let remainder = remainder.strip_prefix('\n').unwrap_or(remainder);
-    Some((remainder, total_lines))
-}
-
 pub struct ResponseStream {
     pub(crate) rx_event: mpsc::Receiver<Result<ResponseEvent>>,
     /// Signals the mapper task that the consumer stopped polling before the