Here I am sharing you the code to show a product search form in woocommerce category page. You need to put the code in functions.php page

add_action( 'woocommerce_before_shop_loop', 'my_woocommerce_before_shop_loop' );
function my_woocommerce_before_shop_loop() {
if ( is_tax( 'product_cat' ) ) {?>
<div class="et_pb_row et_pb_row_0 et_pb_equal_columns et_pb_gutters3 productsearch">
<form role="search" method="get" class="woocommerce-product-search" action="<?php echo esc_url( home_url( '/' ) ); ?>">
<label class="screen-reader-text" for="s"><?php _e( 'Search for:', 'woocommerce' ); ?></label>
<input type="search" class="search-field" placeholder="<?php echo esc_attr_x( 'Search Products…', 'placeholder', 'woocommerce' ); ?>" value="<?php echo get_search_query(); ?>" name="s" title="<?php echo esc_attr_x( 'Search for:', 'label', 'woocommerce' ); ?>" />
<input type="submit" value="<?php echo esc_attr_x( 'Search', 'submit button', 'woocommerce' ); ?>" />
<input type="hidden" name="post_type" value="product" />
</form>
</div>
<?php
}
}