@Biondo38 I have the same issue as you and I think I found the issue.
I think what you meant is that you cannot see the recurring birthday events in the Outlook calendar for those contacts that have been synced through the "iCloud for Windows"app.
If that is so, I found the bug and a workaround consisting of editing the Outlook contact birthday field, change the date to another one, then insert the correct birthdate back again and save the contact: at that moment, a prompt box will be triggered, asking you if you wish to create a birthday event in the calendar! This workaround is obviously time-consuming, but it reveals that there is a bug somewhere that denies the birthdays events to be created automatically in the Outlook calendar unless the birthday field is triggered by a change of date. This indeed seems to occur only for contacts synced through" iCloud for Windows" app. I take it is not Apple's fault but something that has to be corrected by Microsoft as it is not normal that we cannot see contact birthdays in the Outlook calendar when those birthdates are displayed in the contacts...
Below is a screenshot of the prompt you get once resaving the contact (sorry for my French :rolling_on_the_floor_laughing::(