PHP Fatal error: Uncaught Error: Cannot access property started with '\0' in /wp-content/plugins/better-search-replace/includes/class-bsr-db.php:344

It's a known issue on PHP 7.3.
This is because of the empty char which IS NOT exactly an empty character but "*_".
You can't have a property starting with *.

$item->*_tbl becomes $item->\0_tbl. It's from the wp_options in my case.

Btw, solution is:

$key = trim( $key );
$this->$key = ...