But how can I (a voter), audit it in the voting booth? How can I verify that the extensively audited software is actually running on the machine in front of me?
You can't. And even if the software is open source, it doesn't guarantee that state or election officials will set aside budgets to deploy such patches swiftly, or even care to deploy them.
You can't. Especially at scale (every person validating the software before voting). Paper ballots with a anonymised ledger of votes placed is, in my opinion, the best method.
do you think these questions are addressed by open-source software? I mean, if you only have a few buttons in front of you, how can you verify/audit the software it's running?