@Simonas, Thanks for posting in Q&A. Based on my researching, I find for corporate device, Copy and paste between work and personal profiles: have the value of Allow or Not configured.
For Personal device, the setting has value Block and Not configured.
Currently, the setting for COPE does not have Block value. As a workaround, you can create an app protection policy to set "Restrict cut, copy and paste between other apps" as Policy managed apps. to only allow copy paste between policy managed apps.
https://learn.microsoft.com/en-us/mem/intune/apps/app-protection-policy-settings-android
Hope the above information can help.
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