docs: bring README and AGENTS.md current with multiplexing and connection tracing

[andybons]

What

Catches the top-level summary docs up to the features shipped in v0.18.0–v0.20.0. Each feature PR updated its own reference/concept/guide docs; this fills the summary-level gaps those left in README and AGENTS.md.

• README — added a single-port multiplexing callout (same-port trigger, one-LB motivation, links guide 11) and a connection-tracing callout (run_id trusted identity + client-set application_name slug, visible in Neon's pg_stat_activity).
• AGENTS.md — added proxy/proxyproto.go and proxy/demux.go to the architecture tree, and "PROXY protocol" + "Single-port multiplexing" to the Key Capabilities list.

Verified, not assumed

• README's proxy_protocol mentions were already migrated to the per-listener model (proxy.proxy_protocol/postgres.proxy_protocol) in feat(postgres): PROXY protocol support + per-listener proxy_protocol config #55 — left as-is. Zero network.proxy_protocol references remain outside the historical CHANGELOG entries.
• Consistency sweep of the five per-feature docs (guide 11, config reference, observability, postgres concept, guide 13) against the code found no drift — they already agree on the per-listener naming, the multiplexing trigger, and application_name. No edits needed there.

Docs-only; no CHANGELOG version bump (these document already-released features). go build ./... passes.

[claude]

Claude finished @andybons's task in 1m 0s —— View job

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Reviewing PR #59

• Gather context (diff, changed files)
• Review README.md changes
• Review AGENTS.md changes
• Verify claims against code (proxy_protocol naming, multiplexing trigger, application_name)
• Post final review

Summary

Docs-only change (+8/-0 across README.md and AGENTS.md), no code touched. Verified every factual claim in the PR body against the current code rather than taking it on faith:

• Single-port multiplexing (README.md, AGENTS.md): proxy/demux.go's doc comment confirms the same-port trigger, per-connection first-bytes classification (not in the shared accept loop), and "no config flag" — matches the README wording exactly.
• application_name tracing (README.md): proxy/postgres.go:811 sanitizes and records application_name via SanitizeLogValue, and the comment at postgres.go:808 explicitly confirms startupParams is forwarded upstream unmodified — so the "shows up in Neon's own pg_stat_activity" claim holds.
• Anchor link: docs/content/guides/11-load-balancer-proxy-protocol.md#single-load-balancer-one-shared-port exists (line 72 has the matching ## Single load balancer, one shared port heading).
• network.proxy_protocol sweep: confirmed zero remaining references outside CHANGELOG, consistent with the PR body's claim that feat(postgres): PROXY protocol support + per-listener proxy_protocol config #55 already migrated everything to per-listener naming.
• AGENTS.md file tree: proxy/proxyproto.go and proxy/demux.go both exist as described.

No bugs, security issues, or inaccuracies found. The new prose is consistent with the existing style of both docs (feature bullets in Key Capabilities, one-line-per-file in the architecture tree, callout paragraphs in README). Nothing to change here — approving as-is.