You cannot modify the choices of a relationship field by using a load field filter. These can really only be modified by using the method you mentioned https://www.advancedcustomfields.com/resources/acf-fields-relationship-query/
On a taxonomy page, or any page, ACF sends the current post ID as part of the request. I just did a test and here is what is in the $_POST array for the request.
Array ( [paged] => 1 [taxonomy] => [post_type] => [s] => [max] => [min] => [action] => acf/fields/relationship/query [field_key] => field_587ba38bc815c [post_id] => category_4 [nonce] => b12e5fd166 )
In your acf/fields/relationship/query filter you can look at the
post_id value. From this you can get the taxonomy and the term ID. You can then use these values to modify the query args you return from your filter so that only posts in the current term are returned.
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