How to know if get_posts() failed?

Here’s one way to check if there was an DB error within get_posts():

global $EZSQL_ERROR;

$before = isset( $EZSQL_ERROR ) ? count( $EZSQL_ERROR ) : 0;
$posts  = get_posts( $args );
$after  = isset( $EZSQL_ERROR ) ? count( $EZSQL_ERROR ) : 0;

if ( empty( $posts ) && $before < $after ) {
    // ... DB error(s) within get_posts() when it returns an empty array.
}

Here we check the number of wpdb errors before and after the get_posts() call from the global $EZSQL_ERROR errors collector (src).

But I can imagine that this might give a false positive in some cases though, e.g. if we hook a bad db calls within get_posts() that might not be the reason for empty posts array.

Update. I tested this and noticed that $wpdb->last_error is restored after each $wpdb call. I noticed the global $EZSQL_ERROR array within wpdb::print_error() that is not restored but collects the errors. I therefore updated the answer and replaced $wpdb->last_error with $EZSQL_ERROR.