Rewrite taxonomy permalink appended to CPT archive url

There are 2 possible ways to fix the issue with the term’s permalinks (which is currently using the wrong query var name – intvn-cat):

1. Easy. Just set the 3rd parameter for add_rewrite_tag() to intervention_cat=. I.e. add_rewrite_tag( '%intvn-cat%', '(.+)', 'intervention_cat=" );

2. This is what I would actually do – Remove the add_rewrite_tag() part in your code, then replace all of the %intvn-cat% instances with %intervention_cat%.

And then, be sure to flush the rewrite rules by simply visiting the permalink settings admin page.

Additionally, for performance reasons, functions like get_the_terms() (which the results of has been cached), should be used. See https://developer.wordpress.org/reference/functions/wp_get_object_terms/#more-information.