Need to link bookings with information from Microsoft Forms

I'm trying to migrate a system which was previously in Jotforms. In that system there was a fairly complex form that included a booking calendar. The custom questions I can add in Microsoft Bookings are not complex enough and far too limited, so I need Microsoft Forms for gathering the information or it won't be adequate.

I've had a read of a lot of past discussions -- for example, there was some integration of Microsoft Forms/Bookings but it doesn't apply to our use case at all. External users need to book and provide information using a web form, not Microsoft Teams.

If we send a form via email, it is very unlikely that clients will fill it in so I don't think this is a workable solution. It will just cause more issues for employees if they have to follow up with clients before appointments to fill in the information they need.

I've tried creating a Sway that could embed the form and the bookings calendar but apparently that's unsupported. Is there any way of doing this that *is* supported?