[rossitter]

I'm not sure I agree that a distinction needs to be made between the two, certainly not on lines of agency. The "our" in "to our surprise" may or may not correspond to an agent, patient, etc., in the modified clause.

To an agent: "To our surprise, we found them. To our surprise, group A was found by us first."

To a patient: "To our surprise, they found us. To our surprise, we were found by group A."

To neither: "To our surprise, group A found group B. To our surprise, group B was found by group A."

I suppose "to our surprise" is explicit about whose expectations weren't met in a way that "surprisingly" is not. But in a first-person narrative, I imagine most readers would understand "surprisingly" to mean "to my/our surprise."

[teachingassist]

This suggestion is precisely comparable to the passive voice.

There is an intended agent experiencing surprise, and we might under some circumstances agree that we know who the agent is (just as we expect that "the experiment was conducted" by the author as researcher).

But, technically, the agent is obscured and not written, so we can't be completely certain about the writer's intent. Maybe Rosalind Franklin conducted the experiment: we are only led to infer that the author was responsible.

Personally, I generally understand "Surprisingly," to mean "An attentive reader should now be surprised that...".

There's an expectation of general surprise relative to an earlier claim in the text; the writer assumes the reader will be surprised (whether or not the writer was truthfully surprised). I find myself annoyed by this style, whenever I am unsurprised.

[rossitter]

Comparable to one use case of the passive voice, maybe.

What do you mean by "intended agent"? "Agent" has a common definition in linguistics, and an agent is only an agent in the context of a verb, not an overarching narrative. The same referent can be an agent in one sentence but not the next: "We hid. To our surprise we were found by group A." "Group A" is the only agent in the second sentence.

There may be other definitions of "agent" in other contexts, but we're talking about grammatical voice here.

The passive voice is quite simple: the grammatical subject is filled by the patient or theme of a clause, not e.g. the agent. There are many use cases for the passive voice apart from obfuscation, and obfuscation is hardly a necessary result.

I might call "surprisingly" in your interpretation a weasel word in the broad sense. The inference is that the author wants the reader to take up an attitude but is not being forthright about it.

Of course some passive clauses may be weaselly in their own right, but the passive voice is not weaselly by definition.