Check that a slug is present in the get_terms request

If you just want to check if a term with a specific slug exists in the database, then you can use term_exists(). E.g.

<?php if ( term_exists( $cptTax, 'tax1' ) ) : ?>
    Your form here.
<?php endif; ?>

But if you do meant to check if the term is in a specific terms array, then you can use wp_list_filter() like so:

<?php
$found_terms = wp_list_filter( $tax1List, array( // set one or more conditions
    'slug' => $cptTax,
) );

if ( ! empty( $found_terms ) ) : ?>
    Your form here.
<?php endif; ?>

Or you could instead use array_filter() to use your own filter function, like this:

$found_terms = array_filter( $tax1List, function ( $term ) use ( $cptTax ) {
    return ( $cptTax === $term->slug ); // here, set your own custom logic
} );

if ( ! empty( $found_terms ) ) : ?>
    Your form here.
<?php endif; ?>

And just so you know, your custom function (in_array_r()) returned false because get_terms() by default returns an array of objects where each is an instance of the WP_Term class. So basically, the if in your function would need a condition that looks like ( is_object( $item ) && $needle === $item->slug ). However, for simple filtering, I would use the wp_list_filter() above.

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