Watching the release trailer again, the paladin's smite (timestamp 0:56) seems to take two seperate animations to complete, much like other spells. My guess is smite will work like battle master maneuvers, with spell level selection pre-attack and no spell slot spent on a miss.

I'm not sure what that says about reactions, but unless they change the paladin wouldn't be able to smite on an attack of opportunity.

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