If you find that your manually modified taxonomy terms are getting the slug of their parent term appended automatically, try the following snippet.
For example, on the parent blog: Products > Cars have the slugs products > cars-products
On the child blog the slugs get renamed: products > cars-produts-products
this snippet will force rename cars-products-products to cars-products again.
/**
@brief Force changing of a term slug after update.
@since 2021-02-23 14:28:52
**/
add_action( 'threewp_broadcast_wp_update_term', function( $action )
{
ThreeWP_Broadcast()->debug( 'Forcing renaming slug of %s to %s', $action->new_term->term_id, $action->old_term->slug );
wp_update_term( $action->new_term->term_id, $action->new_term->taxonomy, [ 'slug' => $action->old_term->slug ] );
}, 100 );