Using older versions of Outlook for Mac for personal email and calendar
Hi ImreMorocz,
According to your description, you can’t search in Outlook and you have already re-indexed Spotlight. There are many other reasons for Outlook Search not working such as the wrong profile name and so on. You can try following steps according to Outlook for Mac search returns "No Results," and task items are not displayed (microsoft.com) and check whether it will work or not.
If nothing works, you can provide me some screenshots about where & what steps you tried and the result of typing something in search blanks. I will test for you.
Regards,
Rebecca