docs: note published Gitea repository; fix push helper for missing origin

scripts/push-to-gitea.mjs

@@ -71,7 +71,8 @@ const main = async () => {
   const scheme = base.split('://')[0];
   const host = base.split('://')[1];
   const authUrl = `${scheme}://${encodeURIComponent(login)}:${encodeURIComponent(token)}@${host}/${login}/${repo}.git`;
-  git(['remote', 'remove', 'origin']);
+  const remotes = spawnSync('git', ['remote'], { encoding: 'utf8' }).stdout || '';
+  if (/\borigin\b/.test(remotes)) git(['remote', 'remove', 'origin']);
   git(['remote', 'add', 'origin', authUrl]);
   try {
     const pushed = git(['push', '-u', 'origin', 'HEAD:main']);