single org behavior is linked in the comment above.
Multi-Org SFMC setups, as well as multiple BUs in Single Org (there is no difference in this regard) simply do not work with the standard MC Connect offering.
In the words of the documentation
"Marketing Cloud Connect does not support business unit-level unsubscribes for Enterprise 2.0 accounts. Subscribers are included in the All Subscribers list at the enterprise level and unsubscribed from all business units in the enterprise"
As you rightly state, there is only one "HasOptedOutOfEmail" field. In a multi BU setup, what actually happens is the following:
No matter where you unsubscribe, and no matter what setting that BU has, any logUnsubEvent unsubscription will set this field to "true". I have tested this and documented it step by step because the first time I saw it, I couldn't believe it (and the docs weren't so explicit at the time).
The alternative is not to stop using LogUnsubEvent, though, as this is the only way your unsubs create statistics, work with Einstein etc. Also, it is the only way you stay consistent with other standards - no matter your custom implementation, List-unsubscribe Header in Commercial Emails will keep logging unsub events and will keep setting "HasOptedOutOfEmail" to true. So you can't really stop it from reoccuring. I have no official statistics on this, but I checked in some implementations and saw up to 10% list-unsubscriptions, so this does carry some weight.
So the alternative - in my book - must be to let the connector do its thing quietly, forget about the standard field, potentially hide it, forget about campaigns and reports for sendout segmentation, create a custom preference center and make sure your permissions are still logged (LogUnsubevent), tracked etc. in a custom implementation.
If you do not want or cannot stop using campaigns and reports for sendout segmentation, then make sure that this implementation also controls "HasOptedOutOfEmail" and reverts it to "false" after keeping track of your unsubscriptions and enforcing their intended effect (a more targeted unsubscription) in other ways.