By that definition a DX7 isn’t a hardware synth. Or a D-50.
I just think of hardware synths as electronic instruments that can produce sound without the aid of an external computer. The Fairlight CMIs and the Synclaviers and the like sometimes looked like mini mainframes but they were essentially workstation synths. The computery bits were part of the system, not some generic host like a PC loading virtual instruments is.
Very few would argue that the Virus TI is a hardware synth, even though on a technical level it’s a bespoke music computer. You can take it wherever there’s power and make music with it in the absence of any computers.
Yeah, the line between a hardware synthesizer, i.e. a synth that makes sounds using hardware components, and a more modern synthesizer, that generates sounds using software algorithms, is becoming more and more blurry.
Personally I have my favorite synthesizers and some are older than dirt, some are analog/digital intermediaries and some are pure software. Likely everyone have their personal favorites, and I am sure they don’t necessarily correspond to mine.
I really do think that the question ought to be related to the sound generated, which after all is the reason we need more than one synthesizer in the first place.
