fatal error

It look like your database is messed upped. Did you restored from a backup? Or did a migration? Switched to another theme?

correct. I do use Updraft Plus Backup plugin. Before every plugin update I always do a backup and if I notice anything strange, I always restore back until the problem has been solved. So there is definitely a restore from time to time.

Do you have a solution on how this can be solved? Or how can I completely remove your plugin from my website and all database entries, so I can cleanly re-install it again?

It is likely a problem with the serialized data. Sometimes this happens with imports from a backup or a (badly written) replace plugin for the database. It could be a wrong charset of the import file or a unsufficient max allowed file size.
If you want to completely remove the plugin from the database the remove alle row in wp_postmeta with meta_key _backorder_max or _backorder_description. And in the wp_options table remove everything where the option_name starts with wcbm_ (wcbm_backorder_report_order_statuses, wcbm_backorder_mail_notification, wcbm_show_available_items).

thank you. I have removed the database rows and reinstalled the plugin. I will now wait for the next orders with backordered items and check if it shows any fatal errors.

after checking, your plugin still shows fatal errors all over again. It has been purged from the website and database completely and still after installing it again now I start to see the same fatal errors again.

There were no database or backup restorations, migrations, or any kind of switch to a different theme.

2022-01-22T10:57:48+00:00 CRITICAL Uncaught TypeError: strpos(): Argument #1 ($haystack) must be of type string, array given in /data/f/c/fc2fe6bd-5916-44b4-b9c0-13c5319e4e79/XXXXX/web/wp-content/plugins/woo-backorder-manager-pro/woo-backorder-manager-pro.php:669
Stack trace:
#0 /data/f/c/fc2fe6bd-5916-44b4-b9c0-13c5319e4e79/XXXXX/web/wp-content/plugins/woo-backorder-manager-pro/woo-backorder-manager-pro.php(669): strpos(Array, '%available%')
#1 /data/f/c/fc2fe6bd-5916-44b4-b9c0-13c5319e4e79/XXXXX/web/wp-includes/class-wp-hook.php(303): WooBackorderManagerPro->wcbm_get_availability_text('', Object(WC_Product_Variable))
#2 /data/f/c/fc2fe6bd-5916-44b4-b9c0-13c5319e4e79/XXXXX/web/wp-includes/plugin.php(189): WP_Hook->apply_filters('', Array)
#3 /data/f/c/fc2fe6bd-5916-44b4-b9c0-13c5319e4e79/XXXXX/web/wp-content/plugins/woocommerce/includes/abstracts/abstract-wc-product.php(2082): apply_filters('woocommerce_get...', '', Object(WC_Product_Variable))
#4 /data/f/c/fc2fe6bd-5916-44b4-b9c0-13c5319e4e79/XXXXX/web/wp-content/plugins/woocommerce/includes/abstracts/abstract-wc-product.php(2058): WC_Product->get_availability_text()
#5 /data/f/c/fc2fe6bd-5916-44b4-b9c0-13c5319e4e79/XXXXX/web/wp-content/plugins/woocommerce/includes/wc-template-functions.php(3515): WC_Product->get_availability()
#6 /data/f/c/fc2fe6bd-5916-44b4-b9c0-13c5319e4e79/XXXXX/web/wp-content/plugins/et-core-plugin/app/models/customizer/class-ajax-search.php(313): wc_get_stock_html(Object(WC_Product_Variable))
#7 /data/f/c/fc2fe6bd-5916-44b4-b9c0-13c5319e4e79/XXXXX/web/wp-includes/class-wp-hook.php(303): Etheme_ajax_search->search_results('')
#8 /data/f/c/fc2fe6bd-5916-44b4-b9c0-13c5319e4e79/XXXXX/web/wp-includes/class-wp-hook.php(327): WP_Hook->apply_filters('', Array)
#9 /data/f/c/fc2fe6bd-5916-44b4-b9c0-13c5319e4e79/XXXXX/web/wp-includes/plugin.php(470): WP_Hook->do_action(Array)
#10 /data/f/c/fc2fe6bd-5916-44b4-b9c0-13c5319e4e79/XXXXX/web/wp-admin/admin-ajax.php(202): do_action('wp_ajax_nopriv_...')
#11 {main}
  thrown in /data/f/c/fc2fe6bd-5916-44b4-b9c0-13c5319e4e79/XXXXX/web/wp-content/plugins/woo-backorder-manager-pro/woo-backorder-manager-pro.php on line 669