I've set foot in a machine shop every day for 25 years, but I'm not
going to make a video to prove it to you. I'll assume that means you'll
choose to continue to doubt me. That's fine, but if you aren't aware
that solid carbide can cut through a tap, I'd say you're the one who's
only peered into the window of a shop on your way to whatever it is you
do.

Google something like "remove broken tap" and you'll see all manner of
references to drilling or milling them out with carbide tools. Maybe
you'll even find a video.

First there is no doubt that carbide can cut hardened steel however
carbide made for steel is extremely brittle. The intermittent cuts
that would take place for 90% of all broken taps would make it a bad
and expensive choice.

Second, nice try at deflecting your response to the OPs question