And it would be great to have more than one incognito mode for that purpose precisely (to be able to run more than two sessions).

Chrome has "profiles" you can use to log into multiple sessions simultaneously. Not sure if you can combine it with incognito mode.

I use QupZilla because this is its default configuration (every window is a separate multi-tab [incognito] session). Not so great last time I checked on the Mac but one of my favorites on the PC.

https://www.qupzilla.com/

AFAIR on Chrome the session does not propagate between the tabs that don't share history (i.e. separately created, not one spawned by the other).

Session is shared across all incognito tabs. Firefox behaves the same way. Even if you close any incognito tabs and then open a new one, it's still on the same session. You need to completely restart the browser (or explicitly clear history) to clear.

Are you sure of that? When I have an amazon tab with a basket full, create a new tab and go on amazon I see the same basket.

I don't have Chrome on the machine I'm using now so someone else needs to check it. But I vaguely remember running at work several sessions to the same service in separate incognito windows and maybe even in multiple tabs of the same window. Now that I think of it, I'm not sure about the latter scenario.

Both scenarios use the same session.

Shares them across all incognito tabs for me.