Problem with arduino ethernet shield

Good morning,
Recently I bought an arduino ethernet shield w5100 R3 to be able to connect my arduino with home assistant through the network.
In my installation I also have an ESP8266 nodemcu that communicates with home assistant through the addon esphome.
I have searched for information but I can not find how to communicate my arduino + ethernet shield with home assistant, is there an addon to do it that is similar to esphome?
Is it possible to modify or save sketch in arduino via ethernet?

Good afternoon, can not anyone help me?

Have you found a solution ?

Cause I’m interested too.