The “painting” is taking place either in additional context or in assumptions the reader is bringing into the interpretation. It is not present in the bare text.

It’s an ungenerous interpretation to suggest that people using “Surprisingly,” are immodest/imprecise/etc.. I could as easily hold the interpretation that “To our surprise…,” is the author trading my time in an attempt to get himself some goodwill from readers. However, that would be equally ungenerous.

How is "to our surprise" trading your time compared to "Surprisingly"? Is it because it contains more words?

The modesty here is about saying "We're not sure if this is generally surprising for everyone, but we were surprised". "Surprisingly" is a bit less conservative to me, its more of a "We think this is generally surprising for the field". I would personally use it only if I knew something has already surprised multiple research groups

The point isn’t how, but that the idea isn’t in the words. If I held that view, I’d be bringing in assumptions into the words that aren’t actually there in the words. This is true even if the author actually had those thoughts. The words simply don’t carry that information.

Human language is a social construct, and words carry whatever information users have decided to assign to it. Looks like quite a few language users disagree with you