So - I’d push back in two ways - a fairly large number of academic philosophers self-identify into one of those two camps. (If you go to their official insti bio pages). They may cross over in their research, but they frequently anchor themselves in one tradition or another.
And, even with the rise of departments that are (nominally) “integrated”, there has been a steady decline of the self-identified continental folks in the US - in TT and tenured positions. I think that’s partly cos they all went over go to the other humanities as part of the post-structuralist/critical theorist wave (ugh).
Finally, just because the dichotomy does apply cleanly doesn’t mean that it doesn’t exist. The characteristic emphases are sort of obvious…
The analytic side tends to prioritize clarity, argument, logic, precision, problem solving etc.
The conti side tends to be more “fuzzy” (my sophisticated technical term 🧐) - and focuses on stuff like meaning (non-linguistic), history, existence, critique, interpretation, narrative etc.
There is also a tendency in the analytic side to see philosophy as continuous with science & math. Progress (fwiw) happens by sharpening/formalizing questions and resolving (discrete) problems through careful logic/argument.
That is very diff from the conti side - where they tend to see philosophy as continuous with literature/history/culture not scimath. Progress (again fwiw) happens by better understanding of human existence/historical situation etc and creating (structures of?) meaning via interpretation/critique.
You could over-simplify this and simply say that the diffs can be characterized by certain key questions asked, like…
Analytic: how exactly is this claim justified?
Conti: what does this reveal about our situation in the world?
Some of this is covered in the podcast - with Nietzche as a key exemplar of the conti tradition.