对于仍然在这里寻找解决方案的人，我能够通过使用launchWebAuthFlow和手动处理OAuth登录来绕过这个限制。
下面的代码片段：

const getGoogleAuthCredential = () => {
  return new Promise<ReturnType<typeof GoogleAuthProvider.credential>>(
    (resolve, reject) => {
      const redirectUri = chrome.identity.getRedirectURL();
      const authUrl = `https://accounts.google.com/o/oauth2/auth?client_id=${oauthClientId}&response_type=token&redirect_uri=${encodeURIComponent(
        redirectUri
      )}&scope=${encodeURIComponent(oauthClientScopes.join(" "))}`;
      chrome.identity.launchWebAuthFlow(
        { url: authUrl, interactive: true },
        (responseUrl) => {
          if (chrome.runtime.lastError) {
            reject(chrome.runtime.lastError);
          }
          if (!responseUrl) {
            reject("No response URL returned");
            return;
          }
          const params = new URLSearchParams(
            new URL(responseUrl).hash.slice(1)
          );
          const token = params.get("access_token");
          if (!token) {
            reject("No token found in the response");
            return;
          }
          const credential = GoogleAuthProvider.credential(null, token);
          resolve(credential);
        }
      );
    }
  );
};

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希望这有帮助！