The whole foundation of the strategy that gives rise to these voter suppression laws is to avoid exactly that direct, causal link. The recent Supreme Court case Chamber of Commerce v. New York reaffirmed that it's not legitimate to simply target voters that don't agree with you. So you're essentially asking to be shown the ways in which people executing this strategy have failed to maintain the necessary cover.
This requires that we acknowledge that such a standard runs counter to the legal standard which includes, from that same case:
...we are “not required to exhibit a naiveté from which ordinary citizens are free.”
United States v. Stanchich, 550 F. 2d 1294, 1300 (CA2 1977) (Friendly, J.)
For the purposes of the law, it is enough that we take their word for their own motives, most damningly from the former RNC Redistricting Chair, Thomas Hofeller - essentially one of their top strategists regarding structuring voting rules:
A switch to the use of citizen voting age population as the redistricting population base for redistricting would be advantageous to Republicans and Non-Hispanic Whites.
This was also the justification for the "citizenship" question on the 2020 Census, and Hofeller's own admission in those files was key evidence for the North Carolina redistricting plan to be thrown out by courts.
The studies that inform these strategies are not published widely, and so for them to be available to you first requires a breach of GOP security (in this case, Hofeller's daughter came into possession of the data after Hofeller's death, where a more secure system would have been to destroy the data or not have it held by a human person).
Other Republican Lawmakers have slipped up, being caught complaining about how certain demographics vote, such as NH House Speaker William O'Brien, bemoaning that college students using same-day registration were:
...kids voting liberal, voting their feelings, with no life experience.
Which, when combined with surges in college student voting, cast Republican efforts to eliminate the ability for college students to register to vote at the campus where they live in a particular light.
Links like this are entirely circumstantial, however, as is most evidence of motive absent explicit admissions such as the Hofeller files.
Everything else that remains is merely empirical data that the fruit of these laws does directly, and disproportionately impact Democrat voters - because it directly, and disproportionately impacts non-white, hispanic, and low SES voters. Making voting require special documents means requiring that voters have the time and resources to obtain those documents. Closing polling locations in minority neighborhoods raises the average amount of time that the act of voting takes - raising the opportunity cost of voting: the wages one might have earned at work instead. The list goes on.
So to review: No, it is highly unlikely you will find data directly linking voter suppression strategies to their impacts. But there is ample data that voter ID laws, the closure of polling places, and other efforts do have these impacts, are championed chiefly by Republicans, opposed chiefly by Democrats, and that Republican strategists do this research for the purposes of informing similar efforts.
That is enough for a reasonable person to conclude that the likelihood of there being a premediated motive in play is sufficiently high.