I’m far from being a Tory, but that’s crap, mate. We do not have a presidential system (thank God - can you imagine President Lettuce Liz?). You do not cast your vote for Sunak, Starmer or any leader (unless you happen to live in their constituency, of course); you cast it for a party in the hope that they will form a government.
When party leader changes mid-stream, I agree that a GE ought to follow on most occasions, though that isn’t the system & both main parties have made the same arguments when changing from Blair to Brown, May to Johnson to Truss to Sunak, or whatever. But in the (incredibly unlikely) scenario set out where a Sunak loses his seat but the Tories win, for once there would not be a lack of mandate.