If you don’t mind tinkering a bit, I have less than $10 invested in controlling both of my garage doors (not including tilt sensors.)
I’m using a Sonoff device which is wifi controlled. It’s designed to be used as a standard wifi enabled switch. But with some hackery it can be made into a dry contact controller using it’s relay. It was surprisingly easy.
I use a simulated button and in core I have it set up to “flash” the sonoff switch once for 500ms when the simulated button is pressed. Using the simulated garage door opener may work better but I haven’t tried yet.
For ~$4.65 a pop these things are great for this and as a smart switch in the home. I can go into more detail if you’d like