I don't know about Rust, but MicroPython runs quite well on the ESP8266/ESP32 boards. Might be worth investigating if you're looking for something a bit more accessible than C.
MicroPython kind of misses the point in this case though. The desire for Rust is for something not only safer and higher level but also fast and low on memory usage. Rust on the esp32 with Rusty bindings to esp-idf would be fantastic.
https://github.com/micropython/micropython-esp32