While the Amendment’s drafters spilled extra ink ensuring that someone who is elevated to the Presidency for more than two years of another President’s term due to that other President’s death or removal from office, it does nothing to clarify that one who is elected twice cannot rise to the Presidency again. In short, if the 22nd Amendment’s purpose was to ensure that there was a 10 year maximum on service for anyone regardless of how they became President, it could have said so.
That’s what I thought, too, But according to that law firm’s (https://cornerstonelaw.us/22nd-amendment-doesnt-say-think-says/) article,
and with our Supreme Court in his pocket…