In my testing I found OBS only needs accessibility enabled. Here's a screenshot of my configuration profile. The code requirement is...
identifier "com.obsproject.obs-studio" and anchor apple generic and certificate 1[field.1.2.840.113635.100.6.2.6] /* exists */ and certificate leaf[field.1.2.840.113635.100.6.1.13] /* exists */ and certificate leaf[subject.OU] = "2MMRE5MTB8"
Hope that helps!

In my testing I found OBS only needs accessibility enabled. Here's a screenshot of my configuration profile. The code requirement is...
identifier "com.obsproject.obs-studio" and anchor apple generic and certificate 1[field.1.2.840.113635.100.6.2.6] /* exists */ and certificate leaf[field.1.2.840.113635.100.6.1.13] /* exists */ and certificate leaf[subject.OU] = "2MMRE5MTB8"
Hope that helps!

I'm still getting prompted to Allow. Does this still work for you?