send start time

popup.js

@@ -61,6 +61,7 @@ function startContest() {
   document.getElementById('reset-button').style.display = 'none';
   document.getElementById('messages').innerHTML = '';
   if (showMessages) switchMessages();
+  sendStartTime(startTime);
 }
 
 function endContest() {
@@ -104,13 +105,21 @@ function switchConnectForm() {
   showConnect = !showConnect;
 }
 
+async function sendStartTime(startTime) {
+  const data = await chrome.storage.local.get(['puzzleScoreboard']);
+  if (!data?.puzzleScoreboard || !data.puzzleScoreboard.includes('/message')) return;
+  fetch(data.puzzleScoreboard.replace('/message', '/start'), {
+    method: "post",
+    headers: {'Content-Type': 'application/json'},
+    body: JSON.stringify({startTime}),
+  });
+}
+
 async function scoreboardConnect(puzzleScoreboard) {
   if (puzzleScoreboard.includes('/message')) {
     const resp = await fetch(puzzleScoreboard.replace('/message', '/connect'), {
       method: "post",
-      headers: {
-        'Content-Type': 'application/json',
-      },
+      headers: {'Content-Type': 'application/json'},
     });
     if (resp.status != 200) return {connected: false, error: 'Invalid contest token'};
     const json = await resp.json();