Ensure that the generic binder *actually* provides deep type safety, leveraging templated ComponentApi type #973
Description
@ditman in #968 add templating of ComponentApi by schema type, which added more type safety to Lit.
It seems like the safety we had in React was actually a bit of an illusion - i'm not sure if it was actually properly deep.
I think we may need changes to the generic binder which leverage @ditman 's change - see https://github.com/google/A2UI/pull/970/changes#diff-8a4c7f4ba35c429600314b2595140472db061201b07ac01e914ddb6276b635ac as a prototype of this.