> this product has basically no relation

Sure it does. It synthesizes video from text.

Ok, but is there anything that connects it to the word synthesia beyond a connection to the word synthesis? Synthesia means something more specific.

Is there anything other than the “synthes” that synthesis shares with synthesia , connecting this product to synthesia in particular?

Is synthesia an actual word? I'm not able to find any reference to it that isn't the piano software or this. Are you thinking of synesthesia?

I am thinking of synesthesia, yes.

Thought the piano software was named after that word. Didn’t check the spelling.

“Synthesia” is probably an amalgam of “synthesis,synthetic” and “synesthesia”. You would really have to ask the author to find out.

Edit: It's worth pointing out that while the words look quite alike, they don't mean the same thing,

synthesis: to put together

aesthesia: ability to feel or perceive sensations

Synesthesia isn't specific to just visual experience from auditory stimulus. It really denotes any mix of senses, be it experiencing visuals when listening to music (reported by e.g. LSD users), bodily sensations from colors et.c.