Add ability to manually adjust the running timer's start time

Allows users to retroactively correct the start time of an ongoing timer
without stopping it. A pencil icon in the timer widget opens an inline
time input pre-filled with the current start time; confirming sends the
new time to the backend which validates it is in the past before persisting.

frontend/src/api/timer.ts

@@ -1,6 +1,11 @@
 import apiClient from './client';
 import type { OngoingTimer, TimeEntry } from '@/types';
 
+export interface UpdateTimerPayload {
+  projectId?: string | null;
+  startTime?: string;
+}
+
 export const timerApi = {
   getOngoing: async (): Promise<OngoingTimer | null> => {
     const { data } = await apiClient.get<OngoingTimer | null>('/timer');
@@ -14,10 +19,8 @@ export const timerApi = {
     return data;
   },
 
-  update: async (projectId?: string | null): Promise<OngoingTimer> => {
-    const { data } = await apiClient.put<OngoingTimer>('/timer', {
-      projectId,
-    });
+  update: async (payload: UpdateTimerPayload): Promise<OngoingTimer> => {
+    const { data } = await apiClient.put<OngoingTimer>('/timer', payload);
     return data;
   },