feat: Freeform apply_patch with simple shell output (#4718)

## Summary
This PR is an alternative approach to #4711, but instead of changing our
storage, parses out shell calls in the client and reserializes them on
the fly before we send them out as part of the request.

What this changes:
1. Adds additional serialization logic when the
ApplyPatchToolType::Freeform is in use.
2. Adds a --custom-apply-patch flag to enable this setting on a
session-by-session basis.

This change is delicate, but is not meant to be permanent. It is meant
to be the first step in a migration:
1. (This PR) Add in-flight serialization with config
2. Update model_family default
3. Update serialization logic to store turn outputs in a structured
format, with logic to serialize based on model_family setting.
4. Remove this rewrite in-flight logic.

## Test Plan
- [x] Additional unit tests added
- [x] Integration tests added
- [x] Tested locally

codex-rs/core/src/config.rs

@@ -750,6 +750,7 @@ pub struct ConfigToml {
     pub experimental_use_exec_command_tool: Option<bool>,
     pub experimental_use_unified_exec_tool: Option<bool>,
     pub experimental_use_rmcp_client: Option<bool>,
+    pub experimental_use_freeform_apply_patch: Option<bool>,
 
     pub projects: Option<HashMap<String, ProjectConfig>>,
 
@@ -1111,7 +1112,9 @@ impl Config {
                 .or(cfg.chatgpt_base_url)
                 .unwrap_or("https://chatgpt.com/backend-api/".to_string()),
             include_plan_tool: include_plan_tool.unwrap_or(false),
-            include_apply_patch_tool: include_apply_patch_tool.unwrap_or(false),
+            include_apply_patch_tool: include_apply_patch_tool
+                .or(cfg.experimental_use_freeform_apply_patch)
+                .unwrap_or(false),
             tools_web_search_request,
             use_experimental_streamable_shell_tool: cfg
                 .experimental_use_exec_command_tool