I had a similar situation with my shutter blinds. The company wanted €500 to install a "smart hub" to enable voice control instead of their little remote. To hell with that, I ordered a couple of servos and an esp8266 and 3d printed some little fingers that would press the buttons on the remote and added the whole thing to HomeAssistant via ESPHome. Cost me less than €30.
I disassembled one of our gate opener's remotes, and hooked the button contacts to Raspberry Pi Zero's GPIO pins. Pi runs a tiny go webserver and Cloudflare tunnel. I hit an obscure HTTPS URL (via button on a phone's homescreen), gate opens.
I remember someone posting something about their garage opening whenever they open safari, as Safari replays GET requests from open tabs when it is un-suspended, although can't find the post right now.
Basically, they had your setup exactly, but they leave the tab open in Safari and whenever they open Safari to browse the internet, the garage door opens.
I didn't dare to hook up Pi with garage opener as well. Our gate auto-closes after a configurable delay, but garage does not. If I trigger the garage opener by accident while I'm not at home, the garage stays open for anybody to come in and take stuff. So I'd need some sort of "is garage currently open" sensor, but I want to keep things simple.
It's really pleasing to me how the "analogue loophole" continues to work. Previously, recording music through the Line Out, or what have you. Now, using a robot to press the supplied remote. It's delightful.
