Hi @Adrian Kaczyński ,
Welcome to our forum!
According to your description, i understand that you can not sync Sent folder of Gmail in Outlook, is Sent folder empty?
If so, please go to Gmail.com>Select > Settings>Select the Labels tab>make sure that Show in IMAP is selected for Sent.
Based on the above, it is suggested that you could try to create a new profile(Control Panel>Mail>Show Profiles>add) and add the account for testing to check if there are some differences.
If the issue persists, considering corruption in send/receive settings file may cause this issue, You can try to reset the SRS file to check if there're any differences.(Go to C:\Users%username%\AppData\Roaming\Microsoft\Outlook>Rename the Outlook.srs file to Outlook.srs.old>restart Outlook)
Hope to help you!
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