I have a required field on a form that is Boolean. Two radios (one labeled "off" and the other labeled "on") seems heavy and old fashion. A single checkbox is lighter but doesn't make much sense since this is tagged with a red * as a required field. A toggle switch could work, but is not used elsewhere in the application.
When it's required, and there are only two choices, a radio group makes much more sense.
A radio group allows the user to quickly see the available choices and select one with a minimum of action. Whereas a drop down requires at least two clicks: one to see the possible selections, the other to actually pick something.
I'm not sure why you'd think that was "old fashioned"; nor am I entirely certain what "heavy" means. Either way, a radio selection is the best choice here.
Going further, because it's required, I'd even recommend that you default the selection to the most common choice which would eliminate yet one more action the user would need to take.
I prefer the checkbox, but I agree that there's some
iffyness when making it required, and it's probably not wise to go with a three-state checkbox (empty, check, and box) because
what does that even mean?
Thinking of the SharePoint forms, there are two options for a yes/no field: Radios or Dropdown... Drop down may do the trick for you -- common control, ability to make required and still be able to validate.