Funnily enough, logical deductions or formal theorem proofs can be seen as a set of transformative steps from the initial premises to the conclusion, where no new information is added in the process. Which makes the conclusion (at a stretch) a bit like "just" rephrasing the initial premises.

Not really. Usually during the deduction you have some steps that pull surprising knowledge from the rest of math to support the reasoning or create and prove interesting lemmas.

If you can prove a theorem without any of that, that's a little boring theorem to prove.

I agree with the spirit of your comment, but not the literal fact of it. Sure, interesting proofs require pulling out some interesting knowledge in the reasoning, but notions like "surprising" or "interesting" are about human subjectivity and don't really exist as a property of a deduction. Surprising or interesting knowledge is not somehow new knowledge that wasn't there before, it's just that we didn't see it previously.

Sure, but it's humans that do the deduction. So "surprising" and "interesting" still matters. Especially when you are treating deduction as a parallel to a piece of prose that one might reasonably hope to be surprising and interesting not just repeated rephrasing of main thesis.