Redesign the implementation of "Invite Members" search

⚠ The description is being updated by @bdenkovych.

Resolving this issue should unblock the solution for https://gitlab.com/gitlab-org/gitlab/-/issues/424505.

Related to MR: !147732 (closed)

Implementation plan

• Close Draft: Add project's group users endpoint (!144796 - closed) and Draft: Use group/project ID for invite user modal (!144507 - closed)
• Revert Use group ID instead of root group ID for query (!142920 - merged) and Replace query to get SAML users and service acc... (!138075 - merged)
  • Reverted by !149815 (merged) and !150978 (merged)
• Remove group_user_saml FF: #434464 (closed)
  • /chatops run feature delete group_user_saml --dev --pre --staging --staging-ref --production
• Revert Allow subgroup owner to query SAML users (!141040 - merged)
• Revert Add params and ordering to group users API (!140241 - merged)
• Revert Add an API endpoint for Groups to get users rel... (!134570 - merged)
• Partially revert Allow Service Account to be added to SSO-enforc... (!126059 - merged)
• Reverts Filter suggested users by saml provider in invi... (!63565 - merged) that was related to https://gitlab.com/gitlab-org/gitlab/-/issues/333625