Migrate static Types class to TypeContext

Currently, hardcoded types like `list` are accessed on a namespace class `Types`. This makes it difficult to programmatically construct types with field/method APIs, e.g. adding `append()` as a method of `list`.

We should refactor the injectable types into an interface, and have `BuiltinManager` implement the interface. Then we can thread that object through parts of the code that need to construct such types.

Start by tracing how the static Types namespace is accessed and how BuiltinManager currently provides injectable types. Review the TypeContext design and the field/method APIs before deciding where the object must be threaded. Done means the injectable types use an interface implemented by BuiltinManager and callers can construct types such as list with additional methods.

Written by the indexing model from the issue text.