Should format be optional?

So far this is only used as a return type for to_json which always returns format: _JsonFormatDict so I think it's accurate for that usage. But maybe you mean it could be confused to mean that a data json dictionary always needs format specified? I renamed the classes to make it clearer that these are not general schemas but specific type hints for those functions.

Does that address it?

I'm not sure the best way to do this, but should the type encode that this dictionary only has a top-level "values" key?

Yeah I agree it would be nice and we could use a TypedDict. Unfortunately, these lines in the function allow a dictionary to have more then just values as a top-level key in case data is a dictionary:

    elif isinstance(data, dict):
        if "values" not in data:
            raise KeyError("values expected in data dict, but not present.")
        return data

I think there is currently no way to use a TypedDict with some fixed keys and then allow for arbitrary extra keys, see this discussion over in the mypy repo.

Another question, here you mention: data: Union[np.ndarray, pd.Series]. When I look to where this is used: https://github.com/altair-viz/altair/blob/master/altair/vegalite/v5/api.py#L2411, I cannot understand why we need to be restrictive on the input types from numpy and pandas here. I really like types like DataFrameLike and SupportsGeoInterface for input data features (so we can be flexible on input and restrictive on output).

I tried to define a type hint named ArrayLike1D something that can serve for one-dimensional data of various forms, but not sure if this is possible yet (eg. python/mypy#12280).

Otherwise, maybe something like they define as type hint for the values of a polars series? There they define an ArrayLike type as such (see here:

ArrayLike = Union[
    Sequence[Any],
    "Series",
    "pa.Array",
    "pa.ChunkedArray",
    "np.ndarray",
    "pd.Series",
    "pd.DatetimeIndex",
]

And in the docstring for values of the series they mention:

values : ArrayLike, default None
    One-dimensional data in various forms. Supported are: Sequence, Series,
    pyarrow Array, and numpy ndarray.

I don't think this type-hint is strictly 1D as the docstring suggest, but it can serve as a reference.
Somehow wished it would be possible to include range as well (ref: #2877).

You're right, that's too restrictive. I used the type hints which were already present in the docstring but seems like this function supports anything that the pandas function infer_type can handle. According to their own type hints this is all object so basically everything. I'd suggest that we type hint it the same to be consistent with pandas. Implemented in e974bc9

Btw, the function infer_vegalite_type is used only here. Your link points to the usage of infer_encoding_types.

That is flexible enough, thanks for the change.