Current behaviour
Trigger: Addition of a 'Group custom field value > your-group-picker-custom-field' to Browse Projects permission in a permission scheme.
Causes: All project names of projects using that permission scheme to become viewable by all users.
Already Verified by Atlassian: JST-189143

Expected behaviour
The trigger above would make each project name using that permission scheme to be viewable just by members of groups which names are selectable values in the appropriate context(s) for that project(s).

Research on old issues
Similar issue: JRA-10940 (Closed because of a long inactivity period, but not resolved)
Caused by?: JRA-14670
Related to?: JRA-26659, JRA-23732, JRA-30209, JRA-30783, JRA-43008, JRA-37242
Bugs that may be fixed: JRA-28278, JRA-28523, JRA-19577
Perceived as a bug: JRA-30784

Documentation
The current behaviour should be documented.
Besides other documentation pages, it would be good to add the following phrase under the section Managing Issues via Group Ownership
Note that granting with Browse Projects permission to a 'Group custom field value' will make all project names using that permission scheme to be viewable by all users.