Hide or Replace the WordPress Welcome Panel [ functions.php ]

Disable_the_dashboard_welcome_screen.php

//Disable the dashboard welcome screen
//This will only hide the panel, not replace it with any other content.

add_filter("get_user_metadata", "my_own_welcome_panel", 1, 4);
function my_own_welcome_panel($null, $object_id, $meta_key, $single) {
  if($meta_key === 'my_own_welcome_panel') { return 0; }
}

Show_your_own_panel.php

// You can replace the WP welcome panel with your own content using this snippet.

add_filter("get_user_metadata", "my_own_welcome_panel", 1, 4);
function my_own_welcome_panel($null, $object_id, $meta_key, $single) {
  
	// Only work with the show_welcome_panel
	if($meta_key !== 'show_welcome_panel') { return null; }

	// If the user has already said they don't want to see the panel, don't show it!
	$show_panel = get_user_meta( get_current_user_id(), 'my_own_welcome_panel', true );
	if(empty($show_panel)) { return 0; }

	// Echo your HTML or content here, but make sure to have a link like the following:
	?>
	<a class="welcome-panel-close" href="<?php echo esc_url( admin_url( '?my_own_welcome=0' ) ); ?>"><?php _e('Dismiss this Message'); ?></a>
	<?php

	// Return 0 or else the original welcome panel will show as well.
	return 0;
}

// Add the functionality to update the user's settings with whether or not they have closed the panel
add_action('admin_init', 'my_own_welcome_set_welcome_panel');
function my_own_welcome_set_welcome_panel() {
	if ( isset( $_GET['my_own_welcome'] ) ) {
		update_user_meta( get_current_user_id(), 'my_own_welcome_panel', intval($_GET['my_own_welcome']));
	}
}