Are union/sum types another "basis"? Some languages include syntax for them at the level of structs, others require they be painfully hacked together out of libraries and template metaprogramming (std::variant, though bare unions exist without carrying a tag).
If lists and structures are basis then sum should be too.
I also thought this was a major omission. After using languages with well-supported sum types (mainly Swift and Elm), I find it painful to go back to languages that lack native support.
Also "strings but moreso". e.g. in TCL and bash everything is actually a string even if you can contextually treat it like an integer.
Covering numeric types more in depth could be interesting. It seems to surprise most people when they run into '0123' for octal or '123f' (or is that 'f123'?) for a float, '0xdeadbeef' for hex, or 'b123' for binary (is that right...? you see it so rarely I'm not sure without looking up some examples). And I'm sure there's more: surely people have come up with notations for quarternions, complex numbers, and more.
Somewhat related: I'm surprised we don't see NonZero numbers (NzInts, NzNats, and NzReals, etc). This would seem to avoid a lot of division by zero problems at the type level. I realize this might "back up" checking for zeros into the origin of denominator values, but that seems like it would be an improvement to me.
In the same vein, having a dedicated type for natural (or even Peano) numbers can be quite nice. I've seen some clever use-cases in Haskell and Rust such as statically enforcing bounds checks. Can't have a negative length list!
Rust also has hash sets (implemented internally with a hashmap) and B-Tree sets (implemented internally with a B-Tree map). They aren't really basis though, but in Rust almost nothing is.
I would love to see a series written on representing all these datatypes in JSON.