Replace custom OTA implementation in web_server_base (#9274)

Co-authored-by: Jesse Hills <3060199+jesserockz@users.noreply.github.com>

esphome/components/ota/ota_backend_arduino_rp2040.h

@@ -17,6 +17,9 @@ class ArduinoRP2040OTABackend : public OTABackend {
   OTAResponseTypes end() override;
   void abort() override;
   bool supports_compression() override { return false; }
+
+ private:
+  bool md5_set_{false};
 };
 
 }  // namespace ota