Assign meta_query value to php variable

Sorry if I’m being dumb but your query says that br_type must be equal to esc_attr($values['category']) so to put it in a variable you would just:

$br_type = esc_attr($values['category']);

Or if you want to get it from $query you would look in one of the places mentioned here:

How do I get a meta value from WP_Query?

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