The battery you linked as a spare won’t work with this chainsaw. That was the older 24v battery line from Greenworks. They have 3 different 24v battery lines, which can be confusing. There is the older 24v lithium ion, the Enhanced 24v lithium ion (what this saw uses), and then the G24 lithium ion. None of those are interchangeable because they modify the battery connections to be slightly different. I just bought a whole line of tools from them (trimmer, hedgers, blower, and this saw) and was bummed out to see that they discontinued the 24v enhanced line and replaced it with the G24 line.
If you’re looking for a spare battery, it has to be the Enhanced 24v battery. The Greenworks item number is 29722 (can be found on amazon). Their spec page says that batteries 29722 or 29732 works with their 24v enhanced lines, however, the 29732 battery was never actually put into production. It was supposed to be the 4ah version of the battery, but since they discontinued the line and went with the G24, I doubt we will ever see anything other than the 2ah 29722 version.
Hope that helps with the battery confusion.