The answer is simple:
/search/query/?category_name=general&post_type=customis not a part of WordPress and has been added by a plugin/theme, you need to ask their support or inspect the code to find out
For everything else, if is_search() is true, then it’s a search archive. If is_search() is not true it is not a search archive.
Since all of those URLs have ?s= they are all searching for things, so they are all search archives.
We know this because it shows search.php, and because the body class is:
class="archive search search-results category category-maintenance category-39 logged-in admin-bar customize-support"
You shouldn’t need to know the priority of template to know which template is currently loaded. WordPress shares this information openly if you built the theme correctly, debugging tools will tell you, and you can always put this is the search template at the top of search.php and see if the text appears.