GDRP what? If the machine is owned by the employer, why would GDPR apply here? Which specific part of GDPR applies here?

IANAL, but if the purpose of taking screenshot every 30 minutes is to control the work of the employee you must know that in the EU you have the right to be informed about any measure taken to control you.

If you can convince the judge that taking the screenshot has other purpose then GDPR doesn't apply.

From (2): The WP29 outlines that a DPIA is likely to be required if «a company systematically monitor(s) its employees’ activities, including the monitoring of the employees’ work station, internet activity» since it implies a «systematic monitoring and data concerning vulnerable data subjects» (23), form GDPR and Personal Data Protection in the Employment Context CLAUDIA OGRISEG

In (1) at point 8: the employeer has to inform the employee about: (i) whether and when monitoring is applied. (ii) the purpose of data processing, (iii) the means used for data processing.

https://legalict.com/factsheets/privacy-monitoring-work-gdpr...

Point 2) What king of personal data does an employer process, includes: Remote management of all mobile devices, such as phones and laptops;