Add `type` field for model types (inference, embedding, re-ranking etc)

[slmnsh]

Right now models.dev returns all the models together and the model detail doesn't contain any information about model type.

[github-actions]

This issue needs maintainer review and no automated fix was opened.

The request asks for a new way to classify/differentiate model types (inference vs. embedding) in the API output. This is a schema/feature request rather than a concrete correction to existing model or provider metadata, so it falls outside the scope of automated catalog data fixes. It would require changes to the data schema and likely the core generation logic, which a maintainer should evaluate.

[slmnsh]

I think we can add type in each toml to indicate which type of model (inference, embedding, re-ranking etc) it is.