There's room for these definitions to get fuzzy really fast, as is the case with any genre of any medium, but while the Tunnel Man is a form of meta progression, the game makes it pretty clear that using the tunnels to beat the game isn't beating it "for real". Even using my definition, games like Dead Cells and 20XX blur the line between -likes and -lites a ton.

Been a while since I've played spelunky, is the tunnel man the shortcut to later levels? Because it exists in Shiten the Wanderer and it's definitely still a roguelike. There are small deviations, like this, unlocking companions and keeping a storage room with limited access, but everything else is pretty straightforward roguelike.

That's the thing in the end, no clear definition exists. The "Berlin interpretation" is just a bunch of guidelines, and even the most "roguelikes" of roguelikes deviate a bit from it (stuff like "no modes" is even broken by 3 out of 5 games the interpretation considers "canon").

Personally I consider real time to be a bit of a stretch, but yeah, stuff like spelunky or crypt of the necrodancer blur the line.

Not Hades and Dead Cells though. I love them, but they feel way too different to play for me to consider them the same genre.