Adding on that they also want to overview how the elections are held in addition to the people eligable to vote. In other words: be able to control how Minnesotans vote.

Each state decides how to run its elections.

It usually lists known party affiliations

Correct

and who people voted for that cycle

False

You register to vote and you select a party preference, so you can vote in that party's primary, but all votes are not tied to your individual person.

If you get a ballot in the mail(state dependent option), then you fill out your ballot and sign the back of the envelope that contains the ballot. The envelope is then turned into USPS or you take it to the registrar office, and drop it off. On voting day, ballot counters rip open the envelope, discard the envelope, and then your ballot(which has no markings or references to your individual person/identity) gets fed into a machine.

If you go in person to vote, same thing, you go to a voting location, they check your registration status(are you registered, party preference, etc.) and give you a ballot. You go into a voting booth, fill out the ballot, and then you drop the ballot off into a ballot box. Again, nothing on the ballot is marked or references your person.

Now you can make assumptions that a person registered as a Democrat voted for the Democrat running candidate, but there is no record of who you actually voted for UNLESS ballot counters make mental notes and go through your ballot for the mail-in-ballots, but again, there are people monitoring the ballot counters and I know some places use security cameras to make sure ballots aren't tossed/destroyed. No phones are allowed in the ballot counting area.