* feat(ui): cut playground over to the /ui/playground path route
Follows the api-reference recipe: the sidebar and deep links route
llm-playground to the path route, ?page=llm-playground redirects, and
the legacy switch arm is deleted. The route's page.tsx was already the
real implementation, so no view extraction was needed.
* refactor(ui): move playground-owned files into its route folder
Per the (dashboard) README convention, page-owned code lives in the
page's folder: chat_ui/compareUI/complianceUI components, the chat
hooks, and the playground-only llm_calls helpers move under
(dashboard)/playground/. Modules with non-playground consumers (chat
message primitives; fetch_models, chat_completion, responses_api) stay
at their lowest common ancestor in src/components/{chat_ui,llm_calls}
because legacy pages still import them. eslint-suppressions entries are
re-keyed to the new paths so the grandfathered baseline still applies.
* test(ui): teach sidebar e2e spec about migrated path routes
The sidebar spec asserted ?page=<key> for every item, which the
playground cutover correctly broke: the sidebar now links to
/ui/playground and the legacy URL redirects there. Drive the expected
URL from the migration fixture (now a page-id -> segment map) so
future cutovers only add a fixture entry. Also wrap one import line
in AgentBuilderView.tsx that the move left unformatted; the changed-
files prettier check flagged it.
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