Pagination does not work, I consider fixing or new coding - wordpress

Question

I coded a wordpress-site and since some time the pagination worked fine. Then it stopped working.
I tried different plugins, but no one works. I want to put the pagination in a special place within a self-coded loop. Therefore the plugin of bestwebsoft seemed to be the best, since it offers the option of displaying the pagination by the use of a bit of PHP. But also that does not work. The support of bestwebsoft is not helpful, they only repeat what I can read in the documentation.
My questions:
1) Is there eventually a problem in my loop, that stops the pagination from displaying?
2) Is it a problem that I use "Masonry" for showing the excerpts and order the excerpts in a horicontal manner? Maybe that interferes with the pagination?
<div class="grid" data-masonry='{ "itemSelector": ".grid-item",
"columnWidth": 285, "gutter": 20 }'>
<?php
$args = array(
'post_type' => array('post',
'os_buch_review',
'os_review',
'os_classic_review',
'os_versus',
),
'post_status' => 'publish',
'nopaging' => false,
'posts_per_page' => '20',
'order' => 'DESC',
'orderby' => 'date',
'cat' => '-5738,-1705, -5933',
);
$tk_startteaser_querie = new WP_Query( $args );
if( $tk_startteaser_querie->have_posts() ) :
?>
<?php
while( $tk_startteaser_querie->have_posts() ) :
$tk_startteaser_querie->the_post();
?>
<div class="grid-item">
<a class="linkclass" href="<?php the_permalink(); ?>"></a>
<h3 class="entry-title"><?php the_title(); ?></h3>
<?php
if ( has_post_thumbnail() ) {
the_post_thumbnail('medium');
}
?>
<?php the_excerpt(); ?>
</div><!-- grid-item -->
<?php
endwhile;
if ( function_exists( 'pgntn_display_pagination' ) ) {
pgntn_display_pagination( 'posts' );
}
wp_reset_postdata();
?>
<?php
else :
esc_html_e( 'Derzeit keine Beiträge!', 'text-domain' );
endif;
?>
</div><!--grid-->
I want to have some kind of pagination. I would prefer a self-coded one, but could not do it. Therefore I also would accept a plugin-solution. but nothing works! Most of all i would like to know where the problem is located.

Answer 1

I don't know what is the code in pgntn_display_pagination function but I have modified your code with below one which will work for you.
Kindly check below code.
<div class="grid" data-masonry='{ "itemSelector": ".grid-item",
"columnWidth": 285, "gutter": 20 }'>
<?php
$paged = ( get_query_var( 'paged' ) ) ? get_query_var( 'paged' ) : 1; // get the current page variable and set it
$args = array(
'post_type' => array('post',
'os_buch_review',
'os_review',
'os_classic_review',
'os_versus',
),
'post_status' => 'publish',
'nopaging' => false,
'posts_per_page' => '20',
'order' => 'DESC',
'orderby' => 'date',
'cat' => '-5738,-1705, -5933',
'paged' => $paged // use $paged variable here
);
$tk_startteaser_querie = new WP_Query( $args );
if( $tk_startteaser_querie->have_posts() ) :
?>
<?php
while( $tk_startteaser_querie->have_posts() ) :
$tk_startteaser_querie->the_post();
?>
<div class="grid-item">
<a class="linkclass" href="<?php the_permalink(); ?>"></a>
<h3 class="entry-title"><?php the_title(); ?></h3>
<?php
if ( has_post_thumbnail() ) {
the_post_thumbnail('medium');
}
?>
<?php the_excerpt(); ?>
</div><!-- grid-item -->
<?php
endwhile;
// Below is full code of pagination
echo paginate_links( array(
'base' => str_replace( 999999999, '%#%', esc_url( get_pagenum_link( 999999999 ) ) ),
'total' => $query->max_num_pages,
'current' => max( 1, get_query_var( 'paged' ) ),
'format' => '?paged=%#%',
'show_all' => false,
'type' => 'plain',
'end_size' => 2,
'mid_size' => 1,
'prev_next' => true,
'prev_text' => sprintf( '<i></i> %1$s', __( 'Next', 'text-domain' ) ),
'next_text' => sprintf( '%1$s <i></i>', __( 'Previous', 'text-domain' ) ),
'add_args' => false,
'add_fragment' => '',
) );
wp_reset_postdata();
?>
<?php
else :
esc_html_e( 'Derzeit keine Beiträge!', 'text-domain' );
endif;
?>
</div><!--grid-->