Configuring preferences and options in Outlook.com
Hello Mihály Barosi!
Welcome to the Microsoft Office Community Forum. Thank you for sharing your concern with us today and we hope that all is well.
I totally understand that you have concern about your Outlook.com wherein the sync email option is blank. Let's us check on this together and sort this out. Rest assured, I will do anything that I can to assist you with your concern.
Based on your description, the reason why your sync email option is blank might be because there's a problem on the server. You may observe the behavior by trying again after 24 hours or by using other network for the internet.
Now here's my to answer your questions;
With synchronizing your Gmail to Outlook.com, this is the same with connected accounts on Outlook.com, this option is no longer available on Outlook.com. Microsoft has removed this option since May 10, 2021. In order for you to sync your Gmail account to Outlook is you will need to use the Outlook mail application to access you emails from Gmail. Please refer to this article here for more information. Add your other email accounts to Outlook.com (microsoft.com)
Hope it helps. I look forward to your response.
Sincerely,
ReynaldoB
M365 Consumer Forum Moderator
Microsoft Community