ACF fields not included in REST response during "multiple content type" search

When doing a REST search against multiple content types (with e.g. https://github.com/elevati/wp-api-multiple-posttype), ACF Pro doesn't inject acf field into the search results.

This is because ACF only injects data to a REST response when it sees that the request is coming for a certain known post type: https://github.com/AdvancedCustomFields/acf/blob/ada1e58a2e5564e7d62ded661ebdaf6a153ccb1f/includes/rest-api/class-acf-rest-api.php#L60-L64

Any way to overcome that programmatically? Such as when processing said search request somehow explicitly provide the list of object sub types for which ACF should inject the fields? I would possibly call register_rest_field myself it but I'm not sure how to discover the global ACF_Rest_Api instance.

Start by reading includes/rest-api/class-acf-rest-api.php around lines 60-64 and trace how the ACF_Rest_Api instance handles REST responses for known post types. Reproduce a multiple-content-type search using the linked wp-api-multiple-posttype example, then verify that search results for every requested type include the acf field without requiring an undiscovered global instance.