The first release of the new nav broke the live updates. Then it was apparently fixed.
The second release of the new nav claims that the live updates were enhanced, though currently they don't work at all.
Can it be refixed?
I've figured out that the live updates still work if I choose some specific tags, earlier it happened only on Stack Overflow, due to very high traffic - so maybe it's a bug now?
Either way, this is sorta not a problem for me currently, because the only places I'm tracking new questions is Stack Overflow, where selecting all my favorite tags provides me with fine live updates.
The second site is Meta: there I figured out how to get the live updates by using
[bug] [discussion] [feature-request] [support] - this finely covers any topics on MSE (or on any metas), because questions can't be asked without required tags.