I think the Nest Doorbell (Battery) could be a good option for you, but there are some things to consider. It has quite good local AI (Artificial Intelligence), that is used to identify people, animals, packages, vehicles so you don't get notifications for all movement. That's a big plus. It's not perfect, but it's pretty darn good. However, there is one issue that may or may not be significant for you - how it handles cold weather. Batteries don't handle cold well, in terms of both charging (which wouldn't be an issue for you given you won't be hard wiring it) and in terms of its ability to provide voltage to the device, which would impact you. In cold weather (below around 32F/0C), you're going to start seeing performance problems with the battery and greatly reduced battery life. There are settings to trim down on the number of events that trigger it to wake up and record video, which can help with the battery issues. However, if the area you live in is consistently cold for long periods of time, you're going to be bringing it in to recharge quite a bit. Some are having to do so weekly, or even more often - depending on number of triggered events.
See the below thread for more on the general cold weather issues. Note, much of the discussion there is about the doorbell's inability to charge well while cold when connected to regular doorbell wiring. That wouldn't be a concern for you since you would not be wiring it. However, the battery performance and frequency that you need to take it down and recharge is going to be a factor if you live in a location that has cold winters. Likely, any doorbell that's battery powered will have similar problems, but the Google one is particularly affected, likely because of how much power it takes with the local AI processing that it has.
https://www.googlenestcommunity.com/t5/Cameras-and-Doorbells/Cold-weather-concerns-with-Nest-Doorbel...
