Trying to use a static .a library, but the linker cannot find it

But if you compile micropython against ESP-IDF v3.3 and in PlatformIO you use framework = espidf with the latest platform version, you’re getting ESP-IDF 4.0.1 (refer Releases · platformio/platform-espressif32 · GitHub).

That also makes sense because in v3.3 you have the esp_eth_init() function: Ethernet - - — ESP-IDF Programming Guide release-v3.3 documentation

But that’s not existent in v4.0.1: https://docs.espressif.com/projects/esp-idf/en/v4.0.1/api-reference/network/esp_eth.html

There it’s esp_eth_driver_install and esp_eth_start().

So I guess you need to recompile Micropython against that exact ESP-IDF version with the same sdkconfig configuration as you’re using in the PlaformIO project.