refactor: rewrite session store using pinia and fix start button

app/src/components/game/QuestPart.vue

@@ -1,9 +1,10 @@
 <script setup lang="ts">
 import { computed } from 'vue'
 import MarkdownText from '../MarkdownText.vue'
-import sessionStore from '../../store/session'
+import useSession from '../../store/session'
 import { Task } from '../../types'
 
+const sessionStore = useSession()
 const tasks = computed(() => {
   return sessionStore.session.tasks.map((task: Task) => {
     const prefix = task.completed ? '✓' : '➤'