A related issue is “vote for my preferred candidate, or I’ll abuse you” as a way for husbands to control wives. That’s especially relevant when one party is favored by a majority of men while the other party is favored by a majority of women.

s/husband/boss

Or despot, or ruthless water district rep (lol)

You can also do this today by telling someone to take a picture of their vote by smartphone or you'll shoot them. Millions post a picture of their ballot on high-energy political forums every 2 years already. This hypothetical is unhelpful.

Where I live, ballot are a piece of paper slipped into an envelope (not sealed). It's mandatory to take at least two different ballots before entering a voting booth. You can take a picture with one ballot inside the envelope and switch before leaving the booth.

That's pretty cool.

Where I live phone use is not allowed in the room where the voting is

And "sharing proof of your internet vote" would not be allowed either. Doesn't matter, they have the same problem.

Pole watchers will see you with a phone. They won't see 'the evil person' in the room watching you vote