[codex] Split app-server request processors (#20940)

## Why

The app-server request path had grown around a large
`CodexMessageProcessor` plus separate API wrapper/helper modules. That
made the dependency graph hard to see and forced unrelated request
families to share broad processor state.

This PR makes the split mechanical and command-prefix oriented so
request families own only the dependencies they use.

## What changed

- Replaced `CodexMessageProcessor` with command-prefix request
processors under `app-server/src/request_processors/`.
- Removed the old config, device-key, external-agent-config, and fs API
wrapper files by moving their API handling into processors.
- Split apps, plugins, marketplace, catalog, account, MCP, command exec,
fs, git, feedback, thread, turn, thread goals, and Windows sandbox
handling into dedicated processors.
- Kept shared lifecycle, summary conversion, token usage replay, and
shared error mapping only where multiple processors use them; single-use
helpers were inlined into their owning processor.
- Removed the fallback processor path and moved processor tests to
`_tests` files.

## Validation

- `cargo test -p codex-app-server`
- `cargo check -p codex-app-server`
- `just fix -p codex-app-server`

codex-rs/app-server/src/request_processors/git_processor.rs

@@ -0,0 +1,36 @@
+use super::*;
+
+#[derive(Clone)]
+pub(crate) struct GitRequestProcessor;
+
+impl GitRequestProcessor {
+    pub(crate) fn new() -> Self {
+        Self
+    }
+
+    pub(crate) async fn git_diff_to_remote(
+        &self,
+        params: GitDiffToRemoteParams,
+    ) -> Result<Option<ClientResponsePayload>, JSONRPCErrorError> {
+        self.git_diff_to_origin(params.cwd)
+            .await
+            .map(|response| Some(response.into()))
+    }
+
+    async fn git_diff_to_origin(
+        &self,
+        cwd: PathBuf,
+    ) -> Result<GitDiffToRemoteResponse, JSONRPCErrorError> {
+        git_diff_to_remote(&cwd)
+            .await
+            .map(|value| GitDiffToRemoteResponse {
+                sha: value.sha,
+                diff: value.diff,
+            })
+            .ok_or_else(|| {
+                invalid_request(format!(
+                    "failed to compute git diff to remote for cwd: {cwd:?}"
+                ))
+            })
+    }
+}