feat: add remote management functionality

- Introduced a new route for adding remotes to git worktrees.
- Enhanced the PushToRemoteDialog component to support adding new remotes, including form handling and error management.
- Updated the API client to include an endpoint for adding remotes.
- Modified the worktree state management to track the presence of remotes.
- Improved the list branches handler to check for configured remotes.

This update allows users to easily add remotes through the UI, enhancing the overall git workflow experience.

libs/types/src/index.ts

@@ -330,7 +330,14 @@ export type {
 export { EVENT_HISTORY_VERSION, DEFAULT_EVENT_HISTORY_INDEX } from './event-history.js';
 
 // Worktree and PR types
-export type { PRState, WorktreePRInfo } from './worktree.js';
+export type {
+  PRState,
+  WorktreePRInfo,
+  AddRemoteRequest,
+  AddRemoteResult,
+  AddRemoteResponse,
+  AddRemoteErrorResponse,
+} from './worktree.js';
 export { PR_STATES, validatePRState } from './worktree.js';
 
 // Terminal types

libs/types/src/worktree.ts

@@ -30,3 +30,47 @@ export interface WorktreePRInfo {
   state: PRState;
   createdAt: string;
 }
+
+/**
+ * Request payload for adding a git remote
+ */
+export interface AddRemoteRequest {
+  /** Path to the git worktree/repository */
+  worktreePath: string;
+  /** Name for the remote (e.g., 'origin', 'upstream') */
+  remoteName: string;
+  /** URL of the remote repository (HTTPS, SSH, or git:// protocol) */
+  remoteUrl: string;
+}
+
+/**
+ * Result data from a successful add-remote operation
+ */
+export interface AddRemoteResult {
+  /** Name of the added remote */
+  remoteName: string;
+  /** URL of the added remote */
+  remoteUrl: string;
+  /** Whether the initial fetch was successful */
+  fetched: boolean;
+  /** Human-readable status message */
+  message: string;
+}
+
+/**
+ * Successful response from add-remote endpoint
+ */
+export interface AddRemoteResponse {
+  success: true;
+  result: AddRemoteResult;
+}
+
+/**
+ * Error response from add-remote endpoint
+ */
+export interface AddRemoteErrorResponse {
+  success: false;
+  error: string;
+  /** Optional error code for specific error types (e.g., 'REMOTE_EXISTS') */
+  code?: string;
+}