"Search groups" in both Project & Group members doesn't allow to search for parent groups

Summary

Search groups in both Project members & Group members views doesn't allow to search for parent groups. We have dozens of groups added this way and it's pretty hard to maintain them when we can't search for a parent group to quickly identify which sub-groups where already added, and which are missing (especially when the results can't be sorted by name as well).

Steps to reproduce

• we have a root Market GitLab Group
• within the group, we maintain our member groups in Market / Members sub-group
  • examples:

    • Market / Members / Capabilities / DevOps
https://<gitlab-url>/market/members/capabilities/devops

    • Market / Members / Products / Dashboard
https://<gitlab-url>/market/members/products/dashboard

• such member groups are then added to the root Market group as Developers or Reporters to have access to all the repos
• when we go to Members -> Groups (https://<gitlab-url>/groups/market/-/group_members?tab=groups), we can filter the groups by searching for DevOps or Dashboard directly, but when we try to search for any of their parent groups: Capabilities, Products, Members - we don't get any results

What is the current bug behavior?

When you search for a parent group name (or a part of its name), you won't get any results.

What is the expected correct behavior?

Search groups should take into the consideration the whole group path, including all its parent groups, so e.g. Market / Members / Capabilities / DevOps, not only DevOps.

Relevant logs and/or screenshots

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Results of GitLab environment info

GitLab Enterprise Edition v16.3.5-ee