I think the PCP warning is wrong. Some times false warning is shown by PCP for dynamic class method callback. If you can't find any solution to the warning then you can suppress the warning.

// phpcs:ignore PluginCheck.CodeAnalysis.SettingSanitization.register_settingDynamic
register_setting(
    'ailpg_business_profile',
    'ailpg_contact_emails',
    array(
        'type' => 'string',
        'sanitize_callback' => [$this, 'sanitize_emails'],
        'default' => ''
    )
);