How to implement 2 search forms on the same page in WordPress?

Question

WordPress

How to implement 2 searches on a website in WordPress? One search in header.php, the second in footer.php.
I do a search with a filter, I use labels as a filter.

<form role="search" method="get" id="<?php bloginfo('url'); ?>" action="<?php echo home_url( '/' ) ?>" >
<div class="form_search">
<input type="text"  placeholder="Введите запрос..." value="<?php echo get_search_query() ?>" name="s" id="s">
<select name="tag" form="<?php bloginfo('url'); ?>">
  <option value="product">Товары</option>
  <option value="service">Услуги</option>
</select> 
<button type="submit" id="searchsubmit">Поиск</button>
</div>
</form>

Similarly, I do the same in footer.php. When I start searching for one of the searches, they both work and a trace is displayed in the address bar. options "

site.org/?tag=product&s=&tag=product

duplicates the 2nd search.
How to implement so that the search works only one?