I work on embedded software for EV chargers. When I speak to an outsider, all I do is firmware. When I speak to my fellow software developers, we differentiate between RaspPi code as software and PIC16 code as firmware. When we speak to our hardware people, they insist that it’s all software.
The perception of “it doesn’t change easily/often” is pervasive but subjective.
An embedded device is the alternative to a general purpose computer such as a smartphone or laptop. The users of general purpose computers can decide which applications get run, unlike embedded devices. Of course, other software can limit the user's ability to make those decisions, but that is not an inherent limit of the system, that is an artificial limitation imposed by another person.