For the benefit of the OP, if he considers converting CDs to a phone or memory stick, I'll share my recent experience having no prior familiarity with either iTunes, smart phones or Car Play. That's right--my first smart phone is an iPhone SE (2020) purchased a couple of months ago. That's a story nobody wants to here I'm sure. Anyway, here's what I did:
1) Downloaded iTunes to my laptop. It's free. It's takes a little bit of time to figure it out but not much. Once you figure out how to burn one CD it's just rinse and repeat. I've used Real Player in the past; iTunes is comparable in terms of ease of use.
2) Burned 430 CDs to my laptop hard drive using Apple's AAC format with files about 1/3 the size of Apple's ALAC lossless format. For cars with base stereos like mine, with wind, road and engine noise on top of that, I reckoned ALAC would provide little if any benefit. AAC is purportedly cleaner than MPG without taking up too much additional space, so I went with that middle ground. I still have the CDs and a home audio system for a higher quality listening experience when in the mood. Personal preference and how you use the files would apply to format selection. If I was getting rid of the CDs altogether in lieu of these files for a lifetime I'd have gone with lossless.
This burning step is a time suck and might be the best reason to buy a CD player for the car. On the other hand, having 430 albums at your fingertips has its own advantages. When embarking on a burning marathon, it's good to have something you can multi-task in 3 or 5 minute chunks as you wait for a CD to burn before loading the next.
3) Once that was complete, I imported them to my iPhone. Very easy, very fast, with iTunes preinstalled on the phone. You might have to download that ap to the phone which should be no big deal. Installing a version upgrade certainly was not.
4) Sync the iPhone to the CX-5. I just followed the directions in the car manual. I can't recall if the manual had the usual head fake or not, but the process turned out to be very simple as I recall.
5) Set the audio source to my phone, navigate the music files on the phone's iTunes, and play. I can't imagine a better interface than what the phone provides. I can't speak to how a memory stick in the auxiliary port works.
I bet if you were willing to take on a new short-term hobby (the burn step) you would not regret it. You declutter the car, have more console and cubby room for other stuff, and there's no way you'd have a large number of CDs at your fingertips. If your CD collection is quite small then fugetaboutit--buy a cheap CD player.