Solidremote 12V - 24V Secure Wireless RF Remote Control Relay Switch Universal 2-Channel Receiver with 2 Transmitters for Garage Door Openers, LED Lights etc (KIT-1)

Either fix your wifi or maybe run ethernet out to the gate an switch to a wired ESP32? Failing that and if you wanted a truly independent solution, would this work? https://www.amazon.com/Solidremote-12V-Universal-2-Channel-Transmitters/dp/B01JGDV8UM Just power it from the local gate power and it acts like an add on button. Assuming the claimed rolling code security is accurate. Or is your problem that in your car or on foot near the gate your wifi doesn't reach YOU so that you can use the HA app to open the gate?