financial markets dont trade when the smears happen (NYE)

Early in my career, I had to babysit our FX quoting app through the July 2015 leap second.

And some things do trade 24/7 (though I wish they wouldn't, one auction per minute during US east coast business hours would be totally sufficient for most US markets).

They can happen mid-year too. They usually don't for this reason, but they can.

Depends on the market. Crypto and prediction markets wont stop.