ESPAsyncWebServer VS ESP8266WebServer

Use esp async Webserver https://github.com/me-no-dev/ESPAsyncWebServer

I don't know what you're doing wrong, but maybe you could change to the ESPAsyncWebServer instead of the fork you're using. Since me-no-dev works at espressif, it seems like that's basically the official webserver to use and I don't see that dvarrel did much good to it in their fork.

For something that's supposed to run at home and not be accessible from the broader Internet, you would do this by having your ESP8266 run as a WiFi client in your home internet and then using something like the EspAsynchWebServer library to make it a mini webserver than can receive requests from any browser in any of your home devices.

There is a library called ESPAsynchWebServer that will easilly allow you to run a webserver in your code on the ESP32 and ESP8266 chips with Arduino and if you check their simple example you can see it's reasonably easy to have the code for doing stuff on the hardware side (say, toggle the pin that controlls an LED) as part of the code that receives and processes HTTP requests.

Check out EspAsyncWebServer, it’s documentation will make clear how it would allow you to do this if you use it.

Go get EspAsynchServer. Check here.

I don't know what kind of Arduino you are using, but I would never try to implement a HTTP server that wasn't asynchronous. Typically using https://github.com/me-no-dev/ESPAsyncWebServer

I would make the ESP32 serve up a web page that displays the battery status, and also handle a button click that turns on or off the relay. You are looking at using https://github.com/me-no-dev/ESPAsyncWebServer