But often a problem is that people in one organization can really only check the free/busy time for one of your calendars (the primary calendar associated with that org), and thus end up booking you when you're busy on one of those other calendars.
I'm guessing this is the root problem you're getting at with your comment.
Until the platforms themselves (ie: Office and Google) offer up a native way to indicate that multiple calendars represent your busy time, you're kinda stuck with this problem without employing a third party service.
The good news is there is a solution to this problem -- my own startup[1] has a feature[2] that watches source calendars and creates blocks of time on a target calendar. It offers several different privacy options, such as making the block simply say "Personal Commitment" or "busy" or having it carry through all the event details (but not attendees because that would create a mess).
[1] https://reclaim.ai/ [2] https://reclaim.ai/features/calendar-sync