Well, you won’t really find properties in a .base file…
I mean, a .base file doesn’t hold more properties than your vault and its notes already do 
.
It’ll hold the general configuration of base (filters, sort, view, etc…) but not properties (these are in your notes)
Yes, you can have formula properties but their values only “exists” in a rendered base (as in the .base file or code block, it’s just a formula)
Maybe this feature request could interest you though: Bases: Temporary / Quick Search / Filtering Columns