Explaining the liveness guarantee

You are right that offering a running chain with some probability of eventual finality is indeed valuable and a great argument for most (low-value) transactions. Being on the 57% side as in the Medalla case, you get some assurance regarding safety, so continuing without finality is acceptable.

But what about the unlikely major chain split condition, with n<2f?
Let’s say you’re online in a group of 40% of validators, with 20% of the total nodes being completely offline, and having another partition of 40% you don’t have any contact with.
Shouldn’t the consensus rather halt completely in this case instead of slashing the faulty nodes until you have two separate networks, as stated in the post? If I am not mistaken the Casper FFG paper calls this an open problem.