Hello @Paul14
Getting WiFi coverage to outbuildings (or even distant areas of large homes) is a challenge. The most reliable solution is to run an Ethernet cable to that structure and place an Ethernet-capable access point out there. A Google WiFi unit that has Ethernet ports can be added to your Nest WiFi system and connected back to the primary Nest WiFi Router unit's LAN Ethernet port (through a switched Ethernet network) to provide access beyond the range of the 5GHz mesh interconnect.
Here's a support page with more details on this: https://support.google.com/googlenest/answer/7215624?hl=en
My advice is to put an inexpensive Ethernet switch on each end of a long cable run like this, especially between two buildings, since that will help protect against power surges that may occur (replacing a couple of $20 Ethernet switches is a lot more attractive than having to replace more expensive WiFi access points).
Now, if you absolutely, positively, simply cannot run an Ethernet cable to the other building, there are some more expensive (and much more complex) solutions that use directional wireless half-bridges to create an Ethernet-equivalent. But, I don't recommend going down that path unless you really, really have to – and if you're not comfortable installing and configuring more complex equipment yourself, you would want to consider finding a firm that specializes in this (and be prepared to pay more for it).
