fix(dashboard): derive per-project setup URL from live origin

[rodboev]

Description

The Per-Project Savings empty state currently shows a hardcoded ANTHROPIC_BASE_URL: http://127.0.0.1:8787/p/<project-name>. When the proxy listens on a fallback or custom port, users can copy a broken setup URL from the dashboard. This change derives the hint from the browser's live origin and keeps the existing /p/<project-name> suffix used by per-project savings. Closes #1508.

Related context: #1406 made non-default proxy ports a normal path, which makes the hardcoded dashboard hint user-visible more often.

Type of Change

• Bug fix (non-breaking change that fixes an issue)
• New feature (non-breaking change that adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation update
• Performance improvement
• Code refactoring (no functional changes)

Changes Made

• Replace the static Per-Project Savings setup hint with an Alpine x-text binding that uses window.location.origin.
• Preserve the /p/<project-name> suffix so the displayed path shape stays aligned with the existing per-project routing contract.
• Add a Playwright regression that loads the dashboard from non-default origins and asserts the empty state follows the active page origin instead of 8787.

Testing

• Unit tests pass (uv run pytest tests/test_dashboard_cache_ttl_playwright.py -k "per_project_setup_url_uses_current_origin" -v)
• Unit tests pass (uv run pytest tests/test_owned_asset_encoding.py::test_get_dashboard_html_reads_as_utf8 tests/test_proxy_dashboard_stats_cache.py::test_dashboard_uses_cached_stats_and_lazy_history_feed_polling -v)
• Linting passes (uv run ruff check tests/test_dashboard_cache_ttl_playwright.py)
• Type checking passes (uv run mypy headroom)
• New tests added for new functionality when applicable
• Manual testing performed

Test Output

uv run pytest tests/test_dashboard_cache_ttl_playwright.py -k "per_project_setup_url_uses_current_origin" -v
tests/test_dashboard_cache_ttl_playwright.py::test_dashboard_per_project_setup_url_uses_current_origin PASSED [100%]
================= 1 passed, 1 deselected, 1 warning in 0.82s ==================

uv run pytest tests/test_owned_asset_encoding.py::test_get_dashboard_html_reads_as_utf8 tests/test_proxy_dashboard_stats_cache.py::test_dashboard_uses_cached_stats_and_lazy_history_feed_polling -v
tests/test_owned_asset_encoding.py::test_get_dashboard_html_reads_as_utf8 PASSED [ 50%]
tests/test_proxy_dashboard_stats_cache.py::test_dashboard_uses_cached_stats_and_lazy_history_feed_polling PASSED [100%]
======================== 2 passed, 1 warning in 0.16s =========================

uv run ruff check tests/test_dashboard_cache_ttl_playwright.py
All checks passed!

Real Behavior Proof

• Environment: Playwright Chromium dashboard harness, dashboard template served through the existing route interception used by the dashboard tests, no live provider required.
• Exact command / steps: uv run pytest tests/test_dashboard_cache_ttl_playwright.py -k "per_project_setup_url_uses_current_origin" -v
• Observed result: http://127.0.0.1:8788/dashboard passed with the new current-origin assertion, and origin/main failed the same assertion because the page still rendered ANTHROPIC_BASE_URL: http://127.0.0.1:8787/p/<project-name>. A separate browser check against http://headroom.local:9393/dashboard also passed on the patched branch.
• Not tested: full live headroom proxy --port 8788 browser validation, unless it is run during implementation.

Review Readiness

• I have performed a self-review
• This PR is ready for human review

Checklist

• My code follows the project's style guidelines
• I have performed a self-review of my code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• My changes generate no new warnings
• I have added tests that prove my fix is effective or that my feature works
• New and existing unit tests pass locally with my changes
• I have updated the CHANGELOG.md if applicable

Additional Notes

CHANGELOG.md is intentionally unchanged because this repo generates changelog entries from conventional commits. The documentation checkbox is satisfied by correcting the in-dashboard setup instruction.

[github-actions]

PR governance

This PR follows the template and is marked ready for human review.

[JerrettDavis]

This looks ready. Deriving the empty-state setup hint from window.location.origin fixes alternate-port/dashboard-host deployments without changing the API surface, and the Playwright coverage proves both the non-default port and host cases. CI is green.