web-capture gateway: replace hand-rolled reverse proxy with httputil.ReverseProxy

[staging-devin-ai-integration]

Follow-up from PR #631 review (finding #7).

examples/web-capture/cmd/gateway/proxy.go hand-rolls copyHeaders/streamCopy/flushWriter/hopByHop, duplicating net/http/httputil.ReverseProxy:

• FlushInterval = -1 gives immediate flushing for streaming responses.
• A Director/Rewrite can inject the auth header + rewrite the target URL.
• ModifyResponse can enforce the <400 status gate.

Correctness bonus: the hand-rolled hopByHop list misses headers named in the request's Connection header (RFC 7230 §6.1), which the stdlib strips automatically.

Deferred from PR #631 because the MSE path has bespoke readiness-retry + liveness logic (proxyMSE) layered on the streaming copy; migrating needs care to preserve that behavior and a separate review. Not a behavioral bug today.

[staging-devin-ai-integration]

Closing — gateway code that only exists in PR #631 (not yet merged). Folding the fix into the PR itself.