fix(proxy): detect stale proxy after browser restart + surface /navigate errors

[lordk911]

Problem

When Chrome/Edge is restarted while a cdp-proxy process is already running (very common — users quit/relaunch their browser all the time), the leftover proxy keeps answering /health with connected: true, but its page-level sessions are now dead. The result:

• Page.navigate silently fails for every call
• tabs get stuck on about:blank
• /navigate returns an empty response body (JSON.stringify(undefined)), so the agent calling it has no signal to act on

From the outside this looks like "CDP can do nothing / every web task fails" and it persists for as long as the stale proxy survives.

Root cause: check-deps reuses any proxy that answers /health, never verifying that sessions actually work.

Repro

# 1. Chrome with remote debugging, start the proxy
/Applications/Google\ Chrome.app/Contents/MacOS/Google\ Chrome --remote-debugging-port=9222 &
node scripts/check-deps.mjs          # -> "proxy: ready (Chrome)"

# 2. quit & relaunch Chrome (new PID, same port 9222)

# 3. check again — health still ok, but the proxy is now brain-dead
node scripts/check-deps.mjs          # -> "proxy: ready (Chrome)"  (false positive!)
# /new <url>          -> tab stuck on about:blank
# /navigate <url>     -> ""  (empty body, navigation silently failed)

Fix

1. check-deps.mjs — functional probe in the reuse branch

Before reusing a healthy-looking proxy, run a real new → eval → close round-trip on a throwaway about:blank tab. If it fails, the proxy is stale → pkill -f cdp-proxy.mjs and restart it (the same manual fix the SKILL.md already tells users to do). This makes a browser restart self-healing instead of silently breaking everything.

2. cdp-proxy.mjs — /navigate surfaces errors

When Page.navigate returns a CDP {error} (or no result), return HTTP 502 + the error JSON instead of writing an empty body. Turns an invisible failure into a diagnosable one.

Both changes are minimal and additive (happy path behavior is unchanged — verified: navigate still returns full results, the probe passes on a healthy proxy without spurious restarts and leaves managedTabs at 0).

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