The Sony Xperia 1 iii, 1iv, and 1 v should meet all of OP’s requirements except size, and should have most of the bonus features too. Last year I was able to find a used xperia 1 iii for under $500USD. Sony allows bootloader unlocking so I put LineageOS with microg on it, rooted with magisk, and my phone does any thing I want (as long as that thing doesn’t require Google Play Services).