I raised this same problem in February 2025 - including reporting it via a support ticket (TrackingID#2501060050003330).
At the time I received the standard answer that it is "by design" - my interpretation of this is that the design is flawed and more likely "by omission".
It wouldn't take much for the flag in the ICS message to be flipped to require a response when sent from Microsoft Bookings, but there seems to be no fix on the horizon.
Worse still...
If I go into the meeting in Outlook or Teams calendar, flip the 'Request responses' option to be on and press send, it makes no difference (even if I change something else in the meeting like the title): when I go back into the meeting it still says "You haven't requested responses for this event" and the 'Request responses' switch is back to being 'off'.
The person who booked the event receives updated invitation email messages each time I make such a change, and they are able to RSVP to them, but the RSVP status is never reflected in my Outlook/Teams calendar. If they had previously RSVP'd to say "yes", then an update sent by me makes it look to them as though they haven't RSVP'd and so they do it again, but this still isn't reflected on my Outlook/Teams calendar.
If the person legitimately RSVP's to say they can't attend, then I am left waiting for someone who will never join my meeting.
(There is no way they will ever read the body of the invitation and remember to go to the booking page to cancel - they simply right-click and say 'No'.)
Not only is this a waste of my time, but also denies someone else the opportunity to meet with me.
Please Microsoft fix this. One simple tweak would make this a really useful feature.