Moto G 5G 2024 (anywhere from $140 to $200 USD) is the cheapest phone I've found so far that supposedly allows bootloader unlocking. But you'll need to request unlock codes from Motorola. Supported by Lineage OS and CalyxOS (Calyx has temporarily paused development)

Nothing phone 1 & 2 and CMF 2 also has custom rom support, but its hard to find them now adays, and the 3 and newer doesn't seem to have custom roms bult for them yet.