Considering that this is a means to influence the constituency of the house, (and thus to influence legislative processes), the obvious place to work would be swing states. Specific numbers would be specific to specific election years, and while the main census is only ever 10 years, there is also the ACS which is done yearly, on a rotating basis in various regions. Russia specifically has shown a willingness and able-ness to undertake decades long projects to sow discontent and malice within populations of other nations in order to further a long term agenda. Abuse of census data to cause degredation of quality of service, and thus influence local politics to get politicians they view tractable elected is not a big stretch.
The basic exploit looks like this:
1) The area is already divided nearly 50-50 (since it's a swing state).
2) You tip the balance in favor of your desired candidate, by manipulating census representation, and getting funding directed in otherwise dumb directions. (EG, schools get built in areas that dont need them, while areas that do get shrifted--- etc.) This causes public sentiment to become poisoned.
3) You do this by having agents in the country that serve as centers for the exploit; they accept "houseguests" in the months or weeks prior to the census, and since there are no controls over citizenship status of those residing in the residence, they participate, and cannot be caught. (There is no way to verify, and catch.) They provide information that makes a certain area appear more needing of resources than it actually is, or cause the numbers to become inflated.
4) you get your desired candidates into official positions, and let nature take its course.
I do not have the resources of a foreign government; I am merely approaching this from the same kind of perspective a system architect does when approaching cyber security; A potentially exploitable hole, however small, is still an exploitable hole. Saying 'oh, that's not likely to cause a big disruption', is how you get databases with thousands of people's data leaked, or your data held hostage.
In this case, it's how you sneak in favorable candidates, and poison the legislative process.
Those two governments specifically have shown concerted interest in disrupting and manipulating state elections; It's not tinfoil hattery to express that the need to prevent that before it can happen needs to be taken seriously.
Your request for specific numbers is like a CFO wanting to know the specific chances of the meltdown bug causing a major problem, or in what ways an attacker could use it. Until it happens, that data does not exist.
If you want analogous situations though, you can look at 1800s Kansas/Missouri history, with regard to
the referendum for Kansas to be either a free or slave state. Missouri and Arkansas both (but mostly missouri) had concerted efforts involved to pack ballots in Kansas with people who were not native residents, to influence and sway the vote, due to a lack of quality control measures on assuring validity of voter eligibility, or residency. It nearly worked then.
More recently, there was the
many year long propaganda campaigns (1) (2) from Russia to sow discontent in the Ukraine prior to its annexation of Crimea. (which was done to make the annexation appear more legitimate, and to make the annexed populations tractable.)
There is also of course, the social media and fake news issues of the last presidential election, which prompted the Muller report.
If there is a potential means in, Russia seems more than willing to try it. I would rather they did not.