How to declare STAC Catalog extensions?

As far as I understand, extensions implemented in the STAC Catalog (i.e. STAC extensions) should appear in the stac_extensions field of the STAC API landing page, while STAC API extensions should be listed in the field conformsTo of the same page.

If that's the case, I can't get around how to declare implemented STAC Catalog extension using stac-fastapi.

From a code inspection it looks like this should be possible, in principle, via the extension_schemas argument of the LandingPageMixin._landing_page method here: https://github.com/stac-utils/stac-fastapi/blob/7b209773a9f96b24d570e7c1132711e5e4c84df3/stac_fastapi/types/stac_fastapi/types/core.py#L48

but it also looks like wherever the method is used it is always harcoded to [], i.e. here:
https://github.com/stac-utils/stac-fastapi/blob/7b209773a9f96b24d570e7c1132711e5e4c84df3/stac_fastapi/types/stac_fastapi/types/core.py#L155

and here:
https://github.com/stac-utils/stac-fastapi/blob/7b209773a9f96b24d570e7c1132711e5e4c84df3/stac_fastapi/types/stac_fastapi/types/core.py#L365

What am I missing?

Start in stac_fastapi/types/stac_fastapi/types/core.py by reading LandingPageMixin._landing_page and its uses near the referenced lines. Trace how extension_schemas and conformsTo are populated, then verify the landing page can represent implemented STAC Catalog extensions separately from STAC API extensions.