fix: Ensure event type duplication respects private link setting

[SomayChauhan]

What does this PR do?

Fixes #13389

• This PR takes care of fixing private links duplication when duplicating event types.
• the calendar issue doesn't seem to be connected to event type duplication. Even if you pick a different calendar and save it, when you come back later, it defaults back to the default calendar
  A separate issue [CAL-3042] Odd behavior on copy and on changing calendar #13417 has alredy been created for that
  The calendar the event is tied to (always goes back to default).
• [UPDATE]: the calendar issue (always going back to default), has been fixed in fix: destination calendar selection resetting to default on page reload #13440

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[supalarry]

Amazing work as always Somay! 🚀

I can confirm that your fix works - duplicated event types have the secret URL setup.

However, small comment below about code re-usage. Let me know what you think.

[supalarry]

Tested and works! Great stuff! 🚀