Q: [...] ignore hiss for a minute. How does cassette compare in terms of 'warmth'? Is tape not also an analog format?

A: If you put your cassette on a radiator, it will get warm. If you leave it on the radiator too long, it will melt.

@luka I sometimes use tape, especially through a dodgy cassette player, to add a bit of grime
Never really sure what "warmth" is supposed to mean, but tape will add a bit of distortion and warble which can sound nice depending on taste