I will add more information about ESP32-PICO-D4 later but now I briefly explain how it is useful and easy to use.
I quickly made a web radio consists of ESP32-PICO-D4 and PCM5102A DAC. (This PCB has some error so you can see thin wire jumpers... New modified PCB will reach me soon.) Simply swapping ESP32 module and ESP32-PICO-D4 is enough to make it! Ultra easy!
But web radio board has very limited number of GPIO pinout so I quickly made full-GPIO pinout version! Again it is ultra easy to handle!!
Nice project! I've been using a TTGO micro-32 (same chip) for prototyping (https://github.com/LilyGO/TTGO-Micro32-V2.0).
I'm looking to use this chip directly as you have, with a Proant 440-A antenna. The data sheet shows a matching circuit (C L C) as does this data sheet for the chip.
I note that you do not appear to have any matching circuit. Do you get a good range, or any issues?