well, I think the point of the ad is to assure people that their selection (HOW they voted) is private. "Remember, what happens in the booth, stays in the booth."
One's party registration (if any) and WHETHER one voted or not (yes/no, you voted or not) is indeed public record, easily searchable and accessible publicly.
Maybe the point of this ad is to counter disinfo online, suggesting that HOW one votes is public. It is not!! One's party registration and whether one voted is public, but HOW one votes is private.
I very much agree with you, about the domestic violence component. That's why I found this ad so disturbing. It's as if, the woman could be in danger of emotional or physical violence if her husband knew. I think the ad is saying, your choice is only known to others (including your MAGA husband), only IF you want it to be known and you choose to tell them. or, you can just lie if that's what you want to do. No judgement That's all true, and that's why it's a good ad.
In the US, the National Domestic Violence Hotline is:
ph: 800.799.SAFE (7233)