Improve naming of the client workspaces

[valerybugakov]

Improve client workspaces naming after the re-org based on the proposal in the RFC.
This task should be done after https://github.com/sourcegraph/sourcegraph/issues/21847 to account for workplaces added as a part of client workspaces re-org work.

[github-actions]

Heads up @AlicjaSuska @umpox @valerybugakov @5h1rU @pdubroy - the "team/frontend-platform" label was applied to this issue.