null fields in item search

[StijnCaerts]

Describe the bug
When the fields extension is enabled, the search response will include null for every field that is not defined in an item.

To Reproduce
Steps to reproduce the behavior:

1. Ingest STAC Item with minimal metadata, eg. https://github.com/radiantearth/stac-spec/blob/master/examples/simple-item.json
2. Send GET or POST /search request
3. The response contains null for the following fields of the features:
   • geometry.bbox
   • assets.*.description
   • assets.*.start_datetime
   • assets.*.created
   • ...
   • links[*].title
   • links[*].label

Expected behavior
According to the STAC API Fields extension, a field should not be specified in the search response if it does not apply to an Item.
https://github.com/stac-api-extensions/fields/blob/6662435f98b8fff6e5d8ffa0f212e3241a10bc6f/README.md?plain=1#L58-L61

Additional context
This bug can be solved in the following ways:
Fix it in stac-fastapi-elasticsearch by adding the exclude_unset=True parameter to the .json() call.
https://github.com/stac-utils/stac-fastapi-elasticsearch/blob/5f26c325940761da7ecd86677da7acceea69bb78/stac_fastapi/elasticsearch/stac_fastapi/elasticsearch/core.py#L512

Or fix it in stac-fastapi by adding exclude_unset to the PostFieldsExtension:filter_fields dictionary.
https://github.com/stac-utils/stac-fastapi/blob/09dac221d86fe70035aa6cddbc9a3f0de304aff5/stac_fastapi/extensions/stac_fastapi/extensions/core/fields/request.py#L57-L60

[jonhealy1]

Do you want to make a pr for this here? Theoretically it can be set both places?

[StijnCaerts]

It can only be set in one place, as you can only supply one value for a keyword argument.
Judging from a quick GitHub search, it seems like stac-fastapi-elasticsearch is the only project using the filter_fields property to get the desired output from pydantic, so I'll create a PR here.