I've always wondered how much impact lack of funding for music education in schools has had, where a surprising number of people just don't know what instruments are even called anymore.
But I'm still always surprised when people just don't even know what instruments are called [1]. (It's not their fault, of course).
[1] https://en.wikipedia.org/wiki/Peek_a_Boo_(Lil_Yachty_song)#L...
In most other genres, "producer" is the person in the studio doing the recording, or also commonly, running the team that does the recording and plays the background instruments etc. Eg your big band leader.
In film (and gamedev), "producer" is the "product" head honcho, more like a CTO than an individual contributor. That's not dissimilar to producers of large music productions, but very dissimilar to deadmau5 jamming out a tune in his basement studio.
Another way to look at it is Phil Spector needed 4 entire Beatles to churn out hit record after hit record. Today someone in his position (a person in a studio with lots of gear) (or just a laptop even) can arguably make an entire hit record on their own, without anyone singing or playing an instrument. Is that really a different role? In a way it is, because you're no longer managing people. But in many other ways it isn't - it's using gear to make a record.
Just as the Beatles would be no more than a skiffle band playing bars without George Martin, Stock-Aitken-Waterman is responsible for huge 80s hits from Dead or Alive, Rick Astley, Bananarama, etc..
Not that it matters, in my opinion, a good song is a good song. But sometimes the producer plays the singers and instrumentalists and sometimes it’s more the other way around.
Just to be clear, this isn't the etymology of "producer" in the electronic music sense, it's from the second definition you described: The person doing the recording.
This is because electronic music is largely created largely using tools that were designed to be used on recorded music in the studio such as delays and reverbs. Electronic musicians are called producers because they use the recording studio itself as an instrument (along with synthesizers and samplers). Hip-hop makes this distinction extremely fluid as the person recording the vocals is often the same person making the backing track.
Don Toliver is a producer turned artist, so is Metro Boomin... Ti is doing stand up comedy, and even Rick Ross is vlogging and running a podcast now instead of working on primarily music. Spotify not paying artists has a lot to do with it I'm sure... It's a sign of doom for music if making music becomes worthless, because the only music left will be artificially generated, and any real music connoisseur knows that's just never going to cut it.