fix: resolve all 15 svelte-check type errors

- Type headers as Record<string, string> in apiRequest (client.js)
- Annotate SyncResult on result object, cast catch vars to any (sync.js)
- Widen sync.push param to Partial<Task>[] (endpoints.js)
- Fix parse() return type to reflect {task?: Task} shape (endpoints.js)
- Narrow add() param from Partial<Task> to Task (tasks.js)
- Cast parseAndCreate result to Task (tasks.js)
- Type tasksByProject grouped object as Record<string, Task[]> (tasks.js)

svelte-check now reports 0 errors and 0 warnings.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

opal-web/src/lib/stores/sync.js

@@ -56,7 +56,8 @@ function createSyncStore() {
 				const state = loadSyncState();
 				const queue = getQueue();
 
-				let result = {
+				/** @type {SyncResult} */
+				const result = {
 					pulled: 0,
 					pushed: 0,
 					conflicts_resolved: 0,
@@ -70,7 +71,7 @@ function createSyncStore() {
 						await syncAPI.push(tasks, state.clientId);
 						clearQueue();
 						result.pushed = queue.length;
-					} catch (error) {
+					} catch (/** @type {any} */ error) {
 						result.errors.push(`Failed to push queue: ${error.message}`);
 					}
 				}
@@ -79,7 +80,7 @@ function createSyncStore() {
 					const changes = await syncAPI.getChanges(state.lastSync, state.clientId);
 					result.pulled = changes.length;
 					// TODO: Apply changes to local state
-				} catch (error) {
+				} catch (/** @type {any} */ error) {
 					result.errors.push(`Failed to pull changes: ${error.message}`);
 				}
 
@@ -95,7 +96,7 @@ function createSyncStore() {
 				}));
 
 				return result;
-			} catch (error) {
+			} catch (/** @type {any} */ error) {
 				update(state => ({
 					...state,
 					status: 'error',