Yeah, I share your frustrations. My car(2015) is also annoyingly pre-CarPlay and features several frustrating interactions w/r/t media playback. Fortunately it works pretty well over bluetooth, but as soon as you plug it in problems emerge.
One of those problems sounds similar to what you're experiencing where if I'm playing something back on bluetooth and then plug in, it will stop playback entirely and when I press the source button to switch to USB, it will (sometimes) say 'no other media available' and it can be an ordeal to figure out the right order of operations to get it to playback properly. With my car specifically, there are two source buttons, one for cycling through all sources(which also frustratingly you can't change the cycle order and often have to cycle through 4 options to get back to USB) and another that is supposed to jump to whatever is trying to play audio, whether that is Bluetooth or any device connected into any of the car's USB ports.
It's the second one that seems to cause the most problems for me and sometimes I have to actually unplug and plug back in, press pause-play-pause, cycle through source more than once before it'll work. Again, there is likely a correct order of operations that will ensure it works every time, but coupled with sporadic interface lag, the whole thing is just a mess.
What's more, on top of all that, there might even be a safety feature built-in that is causing some of these problems, I can't confirm that, but sometimes it feels like if I do all this stuff while in PARK it works flawlessly, but if I try to do it while moving it gives me grief.
So I dunno, don't really have any advice for you, just that I share your frustrations. Auto makers, for the most part, suck at computer tech, especially with regards to multimedia playback and control. I feel like the past couple years especially was bad because auto makers were trying to compete with Apple and Google without anywhere near the expertise or savvy to do so. So you get these convoluted systems that interfere as much as they help.