I can confirm that I ran into the same problem just now working on a frontend form for a client. After I updated to Advanced Custom Fields PRO Version: 5.4.0 I got the same error when submitting the form:
Backend fatal error: PHP Fatal error: Call to undefined function get_current_screen() in /advanced-custom-fields-pro/api/api-helpers.php on line 3313
So I think the problem has nothing to do with your specific setup but is a generic problem that was introduced with the latest release of ACF. When I rolled the version back to Version: 184.108.40.206 everything was working fine as before. I will update my version to 5.3.10 since you indicate the problem is not present there.
I hope a fix will be available soon since we don’t want to miss out on all the great new features that are included in 5.4.0 😉 Thanks in advance for solving this!
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