Note that the "if" of a 1st conditional, despite being in the simple present, can be a future event.
If I am sick on Saturday, the team will not have enough players to play.
I could be feeling fine right now, but that doesn't make the "am sick" unreal, because it refers to a future situation. You could even say:
If I'm sick, the team won't have enough players to play on Saturday.
Again, the context means that "if I'm sick" is about Saturday, not right now.
So in this case, you could probably understand Trump's statement as an elision of
If I am elected president, I will have that war settled...
which is a passive voice type-1 conditional talking about what he'll do if he wins the 2024 election. It's clear from context he's talking about the potential future presidency, not the unreal situation of him being president in 2023.
You're right that if he was talking about what he would do if he was president at that moment in 2023, that would be an unreal situation, and so the type 2 would be appropriate.
If I were president, I would have that war settled...
Finally, the 4 types of conditional are a useful learning tool, but they're not really reflective of natural speech. They're useful for constructing sentences, because if you follow the pattern it always works. But native speakers aren't taught conditionals as 4 types, and many conditionals don't fall into those categories.