A “universal” garage door remote upgrade kit would do the job, if a little bit Rube-Goldbergy. In the US, brands like Genie and Skylink. The kits are intended to add remote capability to an existing GD opener by connecting in parallel with a vanilla 2-wire door opener button. I haven’t seen one used for over 30 years, but turns out they still make them. There’s no reason that you couldn’t connect the relay on the device to anything else that could be triggered by a contact-closure, a ZEN relay module from Zooz, e.g. Total BOM cost would be under 100USD, I think.