Your example is unambiguously plural. It's not a good illustration of "they" creating confusion.
It's truly not a problem. I could contrive a reason to talk about a couple (they plural) and a nonbinary person (they singular) and end up with sentences where you don't know which I'm referring to, but the exact same issue happens if I'm telling a story about two "he" or "she" subjects. And it's solved in the same way.
Bad example. Having the 'but' in there introduces ambiguity. We can't tell if Janice is contradicting Bob and saying they both won't be coming, or if it's just Janice speaking for themself.
Agreed it's a bad example. When already using the specific identifier of names, using general identifiers isn't needed, and is rarely done. Most people would just say Bob is coming but Janice can't make it.