I'm afraid you need to change the html in this. It must be a form with a fieldset of radio inputs. Any other markup for this design poses significant accessibility issues
Once that is done you'd need to
- update styling to accessibly hide the inputs and ensure focus visible and checked states work for keyboard users
- update js to only listen for a form submit. The form should not submit until a required radio has been checked
To make this fully accessible there is more to consider as well but that should be enough to get you started
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