[Course unit page] Problems with Content Experiment functional on the Course unit page

If contentstore.new_studio_mfe.use_new_unit_page flag is enabled, the user faces the following problems when working with experiment groups:

• 500 error if a user tries to add Content Experiment xblock in frontend-app-course-authoring MFE:
  
• Content Experiment xblock is rendered incorrectly if xblock has been added in Legacy:

Content Experiment xblock rendering in frontend-app-course-authoring MFE

Content Experiment xblock rendering in Legacy

• User cannot edit Content Experiment xblock
• User can delete Content Experiment xblock
• User can proceed to the Content Experiment, page only from the Group Configurations page

500 error on the Learning MFE page

It occurs when staff adds a content experiment xblock to a unit and publishes the changes. When the user tries to get to the Learning MFE page he gets an error.

The error occurs only when a group has not been added to the block.

Logs:

edx.devstack.lms  |   File "/edx/app/edxapp/edx-platform/openedx/core/djangoapps/courseware_api/views.py", line 615, in get
edx.devstack.lms  |     return Response(sequence.get_metadata(view=view, context=context))
edx.devstack.lms  |   File "/edx/app/edxapp/edx-platform/xmodule/seq_block.py", line 375, in get_metadata
edx.devstack.lms  |     meta = self._get_render_metadata(context, children, prereq_met, prereq_meta_info, banner_text, view)
edx.devstack.lms  |   File "/edx/app/edxapp/edx-platform/xmodule/seq_block.py", line 553, in _get_render_metadata
edx.devstack.lms  |     blocks = self._render_student_view_for_blocks(context, children, fragment, view) if prereq_met else []
edx.devstack.lms  |   File "/edx/app/edxapp/edx-platform/xmodule/seq_block.py", line 763, in _render_student_view_for_blocks
edx.devstack.lms  |     item_type = get_icon(block)
edx.devstack.lms  |   File "/edx/app/edxapp/venvs/edxapp/lib/python3.8/site-packages/edx_django_utils/plugins/pluggable_override.py", line 77, in wrapper
edx.devstack.lms  |     return prev_fn(*args, **kwargs)
edx.devstack.lms  |   File "/edx/app/edxapp/edx-platform/openedx/core/lib/xblock_utils/__init__.py", line 522, in get_icon
edx.devstack.lms  |     return block.get_icon_class()
edx.devstack.lms  |   File "/edx/app/edxapp/edx-platform/xmodule/vertical_block.py", line 254, in get_icon_class
edx.devstack.lms  |     child_classes = {child.get_icon_class() for child in self.get_children()}
edx.devstack.lms  |   File "/edx/app/edxapp/edx-platform/xmodule/vertical_block.py", line 254, in <setcomp>
edx.devstack.lms  |     child_classes = {child.get_icon_class() for child in self.get_children()}
edx.devstack.lms  |   File "/edx/app/edxapp/edx-platform/xmodule/split_test_block.py", line 398, in get_icon_class
edx.devstack.lms  |     return self.child.get_icon_class() if self.child else 'other'
edx.devstack.lms  |   File "/edx/app/edxapp/venvs/edxapp/lib/python3.8/site-packages/django/utils/functional.py", line 57, in __get__
edx.devstack.lms  |     res = instance.__dict__[self.name] = self.func(instance)
edx.devstack.lms  |   File "/edx/app/edxapp/edx-platform/xmodule/split_test_block.py", line 176, in child
edx.devstack.lms  |     if self.child_block is not None:
edx.devstack.lms  |   File "/edx/app/edxapp/venvs/edxapp/lib/python3.8/site-packages/django/utils/functional.py", line 57, in __get__
edx.devstack.lms  |     res = instance.__dict__[self.name] = self.func(instance)
edx.devstack.lms  |   File "/edx/app/edxapp/edx-platform/xmodule/split_test_block.py", line 166, in child_block
edx.devstack.lms  |     child_blocks = self.get_child_blocks()
edx.devstack.lms  |   File "/edx/app/edxapp/edx-platform/xmodule/split_test_block.py", line 216, in get_child_blocks
edx.devstack.lms  |     group_id = self.get_group_id()
edx.devstack.lms  |   File "/edx/app/edxapp/edx-platform/xmodule/split_test_block.py", line 245, in get_group_id
edx.devstack.lms  |     return partitions_service.get_user_group_id_for_partition(user, self.user_partition_id)
edx.devstack.lms  |   File "/edx/app/edxapp/edx-platform/xmodule/partitions/partitions_service.py", line 146, in get_user_group_id_for_partition
edx.devstack.lms  |     raise ValueError(
edx.devstack.lms  | ValueError: Configuration problem!  No user_partition with id -1 in course course-v1:2u+1+1

Reproduce with contentstore.new_studio_mfe.use_new_unit_page enabled, using the Content Experiment flows described in frontend-app-course-authoring. Start with openedx/core/djangoapps/courseware_api/views.py and the xmodule/seq_block.py, vertical_block.py, and split_test_block.py paths shown in the trace. Done means the block can be added, rendered, edited, deleted, opened, and published without the reported errors.