Hello @ARmedic
First, I'm assuming you already have Google WiFi in your house, since Google WiFi is not a WiFi extender for other WiFi systems.
Second, unfortunately, the personally identifiable information filter has replaced the distance in your post with "#" symbols. But, unless it's thirty feet or less, I would not expect it to work reliably. In general, I don't recommend trying to make the 5GHz mesh WiFi link work between buildings. Running Ethernet will be the most reliable way (and if you already have Google WiFi in your house, you can add another Google WiFi unit in your shop that connects back to the primary Google WiFi unit via Ethernet to extend the network), but if you can't make that happen, then a fixed (mounted) long-range WiFi solution would be a better alternative. These have "high gain" (directional) antennas on them, and can be mounted to point directly at either an existing WiFi system (at relatively short range) or a pair of them can be installed and aimed at each other to achieve really long ranges. Once deployed, they act as a sort of "virtual Ethernet" cable between the building, and you can connect another normal WiFi access point in the outbuilding as if it was wired.
