Most custom ROMs don't seem to use the AOSP dialer anyway. I've mostly seen forks with some nice features Google's dialer still lacks (call recording, for one).
AOSP hasn't been a useful Android distribution for years. Luckily, you can make it useful through third party apps like the Simple apps: https://www.simplemobiletools.com/
Yeah, my first thought after reading the article was something like, "so I guess everyone will have to start grabbing phone/SMS apps out of F-Droid now". Annoying, but not that big of a deal, and I suspect the replacements will be better anyways. Worst case, the community and/or individual ROMs just fork the old AOSP versions, which has happened before as Google abandons things.
Most ROMs I see just fork LineageOS, which has a dialer of its own built in already.
Theoretically you can run an AOSP GSI on your phone and yes then you do need to find apps on F-Droid, but I don't think anyone but ROM developers do that.
I use custom fork of AOSP Messaging (on local LineageOS/microG build) with some minor UI tweaks and bugfixes. I have tried all other messaging apps on F-Droid, but every single one of them was broken in some way (mostly regarding MMS support or notifications while in deep sleep) or was missing a key feature (like delivery notifications).
The problem with MMS is that there is no built in system-level support for the protocol on Android, and due to legacy of 3G network/WAP, the protocol is quite odd when compared to modern alternatives.
I'm using Google Voice for my dialer... really hope they don't break this outright though. Have thought it would be nice to replace GV with a FLOSS option I can self-host, but every time I've looked into it, it feels like such a convoluted mess.
AOSP hasn't been a useful Android distribution for years. Luckily, you can make it useful through third party apps like the Simple apps: https://www.simplemobiletools.com/