Show events in my private apple calendar in my work outlook

I want to see calendar entries I made in my private calendar in the calendar app in my works outlook calendar.

Things that I assume are relevant:

• I added my work-email-address as secondary email to my icloud account
• I added my work-email-address as additional email to my contact-entry

Things I tried:

• invite my work-email-address to the events that I would like to see in Outlook - I never receive the invites in my work - email. I assume that is because calendar knows that the address belongs to me (I added it in my icloud account)
• Share the private calendar with my work-email-address - again, I never receive the invitation. I assume for the same reason as above, somehow calendar things that I should not invite myself.

I should add that inviting other email addresses works.

The only thing that seems to work is inviting my work address with a public readonly link to the private calender. I don't get an email with the Invitation (I assume its the same issue as above), but at least I can copy the public URL and add it to Outlook manually.

My question: is this how it is supposed to work? To me it seems as if calender is beeing too smart by not allowing my to invite an email-address that happens to belong to me.

Is there a way to make the first or second try work?

I am not entirely comfortable with sharing the calendar with a public URL (I know its very unlikely to guess the ID)