Linux phones definitely are a thing, but depending on your threat model, they may not be enough. There isn’t a smartphone which is 100% open-source from all hardware, to firmware, to software. But there’s a variety of phones that are known to run Linux. The Google Pixel 3a is known for working very well with Ubuntu Touch. There’s also the PinePhone, Purism phones, and there will be others too that support “desktop Linux” (specified for pedantry, since Android is also a type of Linux I guess).

You also don’t need a smartphone. They do still sell “dumb mobile phones” that just do SMS and phone calls; I’ve bought some recently. You can get them for really cheap too, like in the range of 20 USD/EUR kind of price. I don’t think that particularly contributes to privacy since these phones are also proprietary and easily backdoored, but I suppose then it’s missing out on much of the spyware that smartphones have installed as software. If it’s location data you’re worried about, sticking it in a faraday cage should be good enough, but if you need to receive unexpected calls that won’t work. If you’re paranoid about the mic recording, while I think that would be an unlikely and unfeasible way of spying, you could also physically block that by putting the phone in something soundproof, but again you’d need some way to hear that the phone is ringing. For camera paranoia just tape over the camera.