Yes, it is grammatical. You are correct about the object of found: it's the entire clause starting with "Russian…" There are two reasons for the comma.
The comma is conventional in this type of reversed sentence structure
First, it's conventional to separate the subordinate clause from the main clause with a comma in sentences with this "reversed" structure. Here are some examples to illustrate the pattern:
"I dropped the toothpaste," said Tom crestfallenly.
"Kilimnik requested the meeting to deliver in person a peace plan for Ukraine that Manafort acknowledged to the Special Counsel’s Office was a ‘backdoor’ way for Russia to control part of eastern Ukraine," the Mueller report stated. (Source: The Hill.)
Trump aides allowed Saudi and Emirati officials to edit a major speech on energy before he delivered it, a congressional report found. (Source: Business Insider.)
Manafort remained in contact with Kilimnik throughout 2017 and into 2018, the report found. (Source: The Intercept.)
In other words, you should understand the use of the comma in this situation by analogy with the way we use the comma after a direct quotation to introduce the main clause saying who the speaker was. The switch from reported speech to direct speech is strong enough that we feel a need to indicate it with some sort of break, at least when the reported speech is a complete sentence. Saying these sentences aloud, we would usually lower our pitch for the main clause.
The same principle is evident here, where the main clause is stuck in the middle of the subordinate clause:
Before and after the August meeting, the report said, Manafort shared internal polling data with Kilimnik through Manafort deputy Rick Gates. (Source: The Washington Post.)
The comma prevents an ambiguity
Second, without the comma, there is an ambiguity: it can appear that the emails are the object of found, as if the sentence said:
Russian military officers hacked Democratic servers to steal thousands of emails in 2016 that the intelligence community and the special counsel found.
I think most readers would resolve the ambiguity correctly, but the comma helps avoid a garden-path sentence.
Even without an ambiguity, the example sentences with indirect reported speech would all be difficult to parse without the comma. For example, this really is ungrammatical in formal writing:
Trump allowed foreign officials to edit his speech before he delivered it a congressional report found.
Without the comma, it appears that "Trump allowed…" is the main clause, and the reader expects "a congressional report" to fit into that clause somehow, but it doesn't.