Here is the summary of what works from the suggestions so far (based on my controlled trials):
- Creating bookings through "Microsoft Bookings" instead of "Personal book with me" page as suggested by Justin Carrier:
Turns out that meetings scheduled through the original "shared" calendar show up on BOTH my iPhone and MacBook, while the newer bookings made through the "personal" bookings page aren't showing up.
Yes, it works! To clarify what these are, Microsoft Bookings is an individual (calendar with an inbox) app: https://www.microsoft.com/en-us/microsoft-365/business/scheduling-and-booking-app, while "Book with me" is a link on your Outlook calendar.
Bookings app provides a separate email and calendar so that you can identify several people or only yourself as "staff" whose calendars sync and availabilities show up. However, the setup is a little more complicated than the "Book with me". You need to identify your availability under the "default scheduling policy" tab. Also, clients should choose you as the staff they want to meet, even though there is no other option.
In my trial, the appointment through Bookings synced with all Fantastical, iPhone, Mac, and iPad calendars. - ordered based on the speed of synchronization, Fantastical synced first, yet the rest was only 1 min delay.
Again, the appointment through "Book with me" did not show up neither on my Mac nor Fantastical, but did on iOS.
In short, the main problem with Microsoft Outlook Book with me has not been solved for at least a year. This is not an Apple problem because it does work with iOS, not macOS, particularly after the recent MacOS changes after M1. Microsoft has not addressed the issue, still!!!
- "Subscription" to the Outlook Cal on Apple Cal, instead of adding it as an account:
Interestingly, yes, it works! It is slow - with a 5 min or so delay, but it shows up both Bookings and Book With Me appointments. Yet, I do not recommend the subscription as the only Outlook source because it does not show the preference to accept "invited events". If you have an invitation for the ugly sweater party of the freshmen student society through the bulk email, the subscribed calendar does not provide the option to decline any invitation and shows the events on your calendar, as you accepted it.
Conclusion: I hate Microsoft - disappearing notes in OneNote, disaster random signing off OneDrive, horrible "focus" inbox of Outlook, frustrating unsynced calendar, traumatizing figure embedding of Word, nightmare stuck of videos on Powerpoint. Yes, we are scholars, engineers, etc. and always find workarounds. If Microsoft does its job, we might find more time to do our jobs instead.