Carry shell invocation metadata and report executor PATH directories (#49360)

## What changed

- Carry the selected shell and login mode through unified exec using `ShellInvocation`. Use this metadata for shell snapshots and credential brokerage instead of inferring it from command arguments.
- Add `prependPathDirs` to exec-server environment metadata, populated from the executor's package PATH directory. Default to an empty list for older servers and omit empty lists from serialized output.

## Testing

Extend environment metadata round-trip coverage for `prependPathDirs` and the remote exec-server integration test to verify the packaged `codex-path` directory is reported.

GitOrigin-RevId: c571c068effcb305d196a701ad9a335ec7a3f5a2

codex-rs/exec-server-protocol/src/protocol.rs

@@ -6,6 +6,7 @@ use codex_file_system::FileSystemSandboxContext;
 pub use codex_file_system::WalkOptions;
 pub use codex_file_system::WalkOutcome;
 use codex_file_system::WireFileSystemSandboxContext;
+use codex_install_context::InstallContext;
 use codex_network_proxy::ManagedNetworkSandboxContext;
 use codex_network_proxy::RemoteNetworkProxyLaunchConfig;
 use codex_protocol::ThreadId;
@@ -116,6 +117,9 @@ pub struct EnvironmentInfo {
     /// Operating system reported by the executor; absent for legacy exec-servers.
     #[serde(default, skip_serializing_if = "Option::is_none")]
     pub platform_os: Option<String>,
+    /// Executor directories to prepend to `PATH` when missing, in priority order.
+    #[serde(default, skip_serializing_if = "Vec::is_empty")]
+    pub prepend_path_dirs: Vec<PathUri>,
     /// Executor-local default directories for resolving `:tmpdir`, when reported.
     /// On Windows, a command's `TEMP` or `TMP` overrides take precedence.
     #[serde(default, skip_serializing_if = "Option::is_none")]
@@ -252,6 +256,13 @@ impl EnvironmentInfo {
             cwd: cwd.and_then(|cwd| PathUri::from_host_native_path(cwd).ok()),
             user_home_dir: PathUri::from_host_native_path("~").ok(),
             platform_os: Some(std::env::consts::OS.to_string()),
+            prepend_path_dirs: InstallContext::current()
+                .package_layout
+                .as_ref()
+                .and_then(|layout| layout.path_dir.as_ref())
+                .into_iter()
+                .map(PathUri::from_abs_path)
+                .collect(),
             temporary_directories: Some(temporary_directories),
             temp_dir,
             capabilities: EnvironmentCapabilities {
@@ -1372,6 +1383,7 @@ mod tests {
                 cwd: None,
                 user_home_dir: None,
                 platform_os: None,
+                prepend_path_dirs: Vec::new(),
                 temporary_directories: None,
                 temp_dir: None,
                 capabilities: EnvironmentCapabilities::default(),
@@ -1447,6 +1459,7 @@ mod tests {
             "cwd": null,
             "userHomeDir": "file:///C:/Users/remote",
             "platformOs": "windows",
+            "prependPathDirs": ["file:///C:/tools/bin", "file:///D:/tools/bin"],
             "temporaryDirectories": ["file:///C:/Temp", "file:///D:/Temp"],
             "capabilities": {
                 "networkProxyLaunch": false,