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Assuming that this is a tinkerer/hobby project and you know your odds of getting a daily-driver phone out of it aren't good:
You can get various Pi add-ons and USB-addressable cards that supposedly have texting and/or voice call capability. Look up a company called Sixfab. How well they work in practice, I don't know. Be prepared to immerse yourself in a large manual of AT commands and cell phone protocol stuff.
So things seem to be pointing at a pi for now? Yes this is meant as a hobby project but trying to daily drive it as a phone that can make calls(as it is the only feature of a phone that is really mandatory to me) is also amonv my plans
If you're really against Pis, you could get one of the USB-controlled modules and try hooking it up to something like a LattePanda, but that's going to be more expensive.
You could also theoretically get a cell modem chip from a company like Quectel and design the supporting add-on board yourself for any SBC of your choice, but I suspect that's further down the rabbit hole than you want to go.
So, yeah, the Pi is probably the smartest choice if you really want to do your own hardware build instead of just buying a PinePhone.
I think making an "usable" phone (especially one that is able to make calls, etc.) yourself is extremely hard to do, if not impossible.
Many "tinker"-phone startups/ devices, like PinePhone or Librem, who made the phones from scratch or mostly themselves afaik, had huge problems in the beginning with basic functions, like making calls.
There's a project (mainly for kids and students) somewhere to make E-readers themselves, maybe you can start with that?
I'll link it to you if I found it.
That might act as a base.
If you want a good phone that gives off DIY-vibes (modularity, repairability, etc.) but want something proper and modern, then check out Fairphone. Afaik, the FP4 also supports PostmarketOS and other mobile distros.
Remember to take everything I said with a huge grin of salt, since I'm not that well informed in that area of DIY- or Linux phones. A lot of what I said might be wrong, take it only as idea or starting point.
But if you really want to start this project, good luck. You'll need it 🫠
To add, in the US, most service providers will not let a device on their network until it has gone through FCC approval. You can get around this by buying a cell module, which has gone through approval, but most of those are data only last I looked.
Your question reminded my immediately about one of my favorite 35c3 talks Butterbrotdosen-Smartphone - Mein DIY-Smartphone-Bau from 2018-12-29. It is in German language, but has an English translation, too. Maybe it can give you some good starting ideas?
Video: 1080p
Story, Translated with DeepL.com (free version)
I would like to show you how I built a smartphone from a Raspberry PI. The problems and difficulties I encountered and the solutions I found. The project is not yet finished, there are still a few small things missing. Nevertheless, I want to show you my smartphone in the practical sandwich box and tell you how it came about.
I had no idea that building a smartphone could be so complicated. Raspberry Pi + touch display is not all there is to think about in this project. At the moment, the smartphone project lives in a sandwich box and attracts attention on the subway. If the power bank can passthrough, that's an advantage, I've found. Setting up the X and Y axes on the touch display so that you can also use the on-screen keyboard was not so easy. And I had to realize that Landscape is not the right size to work smoothly. Most Linux programs are not directly touch-compatible or require too much memory. Then there were also big challenges! Learning to solder was one of them. First learning how to solder, then learning how to desolder, and then daring to use the PI. I would like to tell you these and other stories about building my smartphone.