BuddyPress doesn’t usually display inside a normal WordPress page automatically. The better approach is to add the actual BuddyPress component pages, such as Members or Messages, directly to your main navigation.
Also check **Settings > BuddyPress > Pages** to make sure the BuddyPress pages are assigned correctly. If /messagerie/ is just a regular page with that title, it won’t show the BuddyPress interface by itself.
Since the term is actually created/deleted and only the admin response fails, this does sound more like BuddyPress interfering with the AJAX response than the taxonomy operation itself.
I’d inspect the browser Network tab for the admin-ajax.php response and compare it with BuddyPress disabled. If there’s extra output, malformed JSON, or a delayed hook firing after wp_delete_term, that should point to the component causing it. Given that it happens with both core and custom taxonomies, the term count may just be exposing a timing/scaling issue rather than being the root cause.