browser: migrate api/playwright.py onto get_browser(), retire is_url_allowed's regex allowlist (#13236 step 6) #16552

Sub-issue of #13236 (ADR-009 steps 3-6), scoped to step 6 only.

What's still hand-rolled

api/playwright.py calls services/playwright_service.py's PlaywrightService/playwright_service()/get_playwright_service() directly (via from services.playwright_service import (get_playwright_service, playwright_service, ...)), not autobot_shared.browser.get_browser(). browser_backends/container.py already wraps this exact stack for the canonical interface — api/playwright.py is a second, parallel path to the same container that bypasses the registry (and, before #16544, bypassed its own URL guard too).

Whether is_url_allowed (api/browser_mcp.py) still exists as a regex allowlist, or has already been retired, needs re-checking at the time this is picked up — api/browser_mcp.py's current docstring says "There is no URL allowlist" but that may describe send_to_browser_vm's own guard rather than every caller; confirm before assuming this half is already done.

Why this needs its own review, not a mechanical migration

The whole router (api/playwright.py) is admin-gated (dependencies=[Depends(check_admin_permission)]) and several of its routes (test_frontend, send_test_message) deliberately target AutoBot's own internal frontend (ServiceURLs.FRONTEND_LOCAL) — they are not public-URL fetches and must keep working after any migration. #13236's own text calls for enumerating real internal-host usage before touching the allowlist, rather than guessing at the exception list.

Acceptance criteria

• Enumerate every route in api/playwright.py and classify each as "arbitrary caller-supplied URL" (should route through get_browser()) vs "deliberately internal, own frontend" (should NOT be forced through the public-URL guard)
• Routes in the first group reach the browser through autobot_shared.browser.get_browser(), not services.playwright_service directly
• Confirm current state of is_url_allowed (api/browser_mcp.py) — retire it if still a live regex allowlist, or close this criterion as already done with the commit that did it, if it's gone
• api/playwright.py has no remaining direct services.playwright_service import for the migrated routes
• Existing playwright route tests stay green

Related

• Parent: browser: migrate callers onto the canonical interface (ADR-009 steps 3-6) — closes the #13204 guard gap #13236 (ADR-009 steps 3-6)
• security(browser): send_to_browser_vm and playwright_service bypass the SSRF/DNS-rebind guard the other browser paths enforce #13204 — playwright_service.py's own missing guard, fixed for capture_screenshot in security(browser): validate the URL in capture_screenshot (#13204) #16544; this step is the architectural migration, not the security gap