In the Q/A section of the one linked above your "I found this other adapter....", there's this:
Question: Does it work on 2004 Toyota Camry?
Answer: Didn't work on my 2003 Avalon. Everything plugged in and it connected to my phone,but nothing played through speakers. Sent it back.
By Todd Hudson on October 31, 2018
I don't see a link prior to that, though from the context, there's supposed to be one above "I found this adapter that looks like it might fit the bill..."
Also, again in the Q/A for the last link you provide:
Question: does it work on 2002 Camry LE?
Answer: I cannot tell you if it works on a Camry but i can say i had to return it because it did not work. The power light did not ever turn on so i had to return it. I originally bought it for my 2003 Avalon
By tee on October 5, 2018
I don't know enough to reverse engineer the head unit, but this should be a simple matter of adding an external input that breaks into the amplifier circuitry. It appears as though us 2018 denizens no longer grab soldering guns, rip into feature-sparse electronics, and create do-it-yourself nirvana...
A great loss to people like me (and possibly you) who are terminally cheap.
Meanwhile, I'm using the Anker Roav SmartChargeF3.
It has downsides. First, the readout is pretty useless, being too small to read in the dark and too dim to read in daylight. It also uses local FM transmission from the Roav to the head unit. This means that I can set it up for reliable use locally, but when traveling, I would have to stop, let the Roav find a suitable (empty) FM channel, then manually tune the head unit to that newly found channel.
Other than that, it offers USB input, bluetooth connectivity to phones, and micro SD card sourcing. I'm too backward to get my phone to play through it, so I use the micro SD disk for my playlists.