Not here in Kansas, either: I’ve been an election worker, and we pick the next ballot off the stack and hand it to you. There are no barcodes or serial numbers on individual ballots, although we do stamp the polling place on each ballot (so one mailed as an advance ballot will have a different marking than one handed out at the poll on election day or one voted in-person at an early-voting site).
For an advance (mail) ballot, the return outer envelope has a serial number and must be signed by the voter; if that check passes, the sealed inner envelope is then handed off to another person to be run through the counting machine.
We do keep track of the count of how many ballots are voted versus left over, void/spoiled, etc.
Part of the difficulty in cross-state database comparisons is how the different states record voter registration information. Kris Kobach’s widely-touted Interstate Voter Registration Crosscheck Program identified voters as potential matches if they shared a first name, last name, and full date of birth. Social Security numbers were not considered, nor were slight variations in name (Steve and Steven were not the same person, e.g.). The program ended as part of a consent agreement with the ACLU, after admitting they’d mishandled personal data and didn’t have proper data security procedures.
Because of differences in naming patterns and the distribution of surnames among African-American, Latinx, and Euro-American voters in the US, matching only on first name, surname, and DOB tends to flag persons of color as potential duplicates more frequently than whites. For example, in the 2000 census, 2.5% of the 211 million self-identified “white” Americans were named Smith, Johnson, Miller, Brown, or Jones. Meanwhile, 8.26% of people identifying themselves as black/African-American had one of the five most common black surnames (Williams, Johnson, Smith, Jones, Brown), and 9.82% of Latinx had one of the five most common Hispanic surnames (Garcia, Rodriguez, Martinez, Hernandez, Lopez). (See most common black, and white and Hispanic surnames.) For another example, the number of Hispanic voters whose legal first name is Angel, Maria, Juan, Jose, or Jesus is very high,even if they go by other names day-to-day.