Can’t vouch for this specific product, but a weatherized AP in the garage with wire back to the house or a directional antenna from the house to the garage would be your best bet. You need WiFi for updates, plus you may find having outdoor coverage leads to using the space more.
https://www.amazon.com/Tupavco-TP542-Panel-WiFi-Antenna/dp/B015QF7EMK
Agreed, likely a directional outdoor wifi antenna for boosting signal over on that part of the building . Quick search it looks like this
Maybe swap one of the router antennas out for a directional antenna and point it to the other location? Something like this for example:
15cm^3 is a pretty tight constraint. I'd probably go with some kind of panel antenna like this for something dialed in around 2.4ghz.
https://www.amazon.com/Tupavco-TP542-Panel-WiFi-Antenna/dp/B015QF7EMK
Get routers/aps with replaceable antennas and get directional antennas. Like such: https://www.amazon.com/Tupavco-TP542-Panel-WiFi-Antenna/dp/B015QF7EMK