[codex] Delete function-style apply_patch (#21651)

## Why

`apply_patch` is now a freeform/custom tool. Keeping the old
JSON/function-style registration and parsing path left another way for
models and tests to invoke `apply_patch`, which made the tool surface
harder to reason about.

## What changed

- Removed the `ApplyPatchToolType::Function` variant, JSON `apply_patch`
spec, and handler support for function payloads.
- Kept `apply_patch_tool_type = freeform` as the supported model
metadata path, including Bedrock catalog metadata.
- Migrated `apply_patch` tests and SSE fixtures to custom/freeform tool
calls.

## Verification

- `cargo test -p codex-tools -p codex-protocol -p codex-model-provider`
- `cargo test -p codex-core tools::handlers::apply_patch --lib`
- `cargo test -p codex-core --test all
apply_patch_tool_executes_and_emits_patch_events`
- `cargo test -p codex-core --test all
apply_patch_reports_parse_diagnostics`
- `cargo test -p codex-exec test_apply_patch_tool`
- `just fix -p codex-core`
- `just fix -p codex-tools -p codex-protocol -p codex-model-provider -p
codex-exec`

codex-rs/tools/src/tool_config.rs

@@ -219,11 +219,10 @@ impl ToolsConfig {
             model_shell_type
         };
 
-        let apply_patch_tool_type = match model_info.apply_patch_tool_type {
-            Some(ApplyPatchToolType::Freeform) => Some(ApplyPatchToolType::Freeform),
-            Some(ApplyPatchToolType::Function) => Some(ApplyPatchToolType::Function),
-            None => include_apply_patch_tool.then_some(ApplyPatchToolType::Function),
-        };
+        let apply_patch_tool_type = model_info
+            .apply_patch_tool_type
+            .clone()
+            .or_else(|| include_apply_patch_tool.then_some(ApplyPatchToolType::Freeform));
 
         let agent_jobs_worker_tools = include_agent_jobs
             && matches!(