Is there an existing issue for this?

• I have searched the existing issues

Problem statement

Multiple UCX installations per workspace cause plenty of problems

• two installations pointing to the same database will corrupt the state, potentially resulting in a data loss
• account admin won't easily be able to update workspace mappings everywhere required
• some commands, like databricks labs ucx sync-workspace-info, databricks labs ucx sync-azure-service-principal-access, and databricks labs ucx sync-aws-role-access are to be executed by IAM/account admins, that don't per-se require a full installation of UCX jobs and dashboards, as they need to push data to existing installation instead
• Potentially unclear error messages related to multiple installations and configurations on the same workspace #350
• [FEATURE]: If UCX installed remotely on the workspace has different version than the one installed locally and we don't launch databricks labs update ucx, simply install UCX locally as the CLI #1072

Proposed Solution

• by default, install into /.ucx (workspace root), giving prompt.confirm("do you want to install ucx just for a user?") to install it in /Users/$currentUser.me/.ucx instead. default name of ucx database should use WorkspaceInstaller._app (username suffix) then
• when being installed on a user level, check other installations and verify that no conflicting databases exist
• introduce InstallationManager.current() to pick installation either from current user or workspace root

Additional Context

No response