feat: Fix Playground admin signup: proxy OpenWebUI /workspace+/auth and route /api/v1 via dashboard

[liavweiss]

Context

This PR is follow-up work for Issue #849 and builds on the previously-merged fix in PR #850.

After pulling #850, testing showed a remaining issue: clicking Create Admin Account consistently fails with a 500 on the /signup API.

Root cause

OpenWebUI is not fully base-path aware when embedded. In the Playground flow it navigates and/or calls root paths (e.g. /workspace, /auth) and related OpenWebUI APIs. Without explicit dashboard backend routing for these root routes + OpenWebUI API endpoints, requests can fall through to the dashboard SPA or a different upstream, resulting in broken signup/admin creation.

Fix

• Frontend: Load OpenWebUI in the Playground iframe via a real OpenWebUI root route (/workspace) rather than a base-path mount.
• Dashboard backend:
  • Proxy OpenWebUI root UI routes needed by the embed (/workspace, /auth) to OpenWebUI.
  • Route OpenWebUI API requests by path (/api/v1/* and /api/config) to OpenWebUI even when the Referer is a root route like /workspace.
  • Preserve Authorization headers when proxying OpenWebUI (forward auth) so authenticated/signup flows work correctly.

Testing

• ✅ http://localhost:8700/playground loads OpenWebUI correctly.
• ✅ Create Admin Account no longer returns 500 and proceeds as expected.

Files changed

• semantic-router/dashboard/frontend/src/pages/PlaygroundPage.tsx
• semantic-router/dashboard/backend/router/router.go

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[github-actions]

👥 vLLM Semantic Team Notification

The following members have been identified for the changed files in this PR and have been automatically assigned:

📁 dashboard

Owners: @JaredforReal, @Xunzhuo
Files changed:

• dashboard/backend/router/router.go
• dashboard/frontend/src/pages/PlaygroundPage.tsx

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🎉 Thanks for your contributions!

This comment was automatically generated based on the OWNER files in the repository.

[Xunzhuo]

thanks!