perf(presence): reduce heartbeat frequency (#3783)

## Summary

- send desktop presence heartbeats every 60 seconds instead of every 30
seconds
- extend presence TTL from 90 to 180 seconds to preserve the existing
three-heartbeat expiry window
- add mutation-sensitive tests that pin the one-minute / three-window
timing contract
- update presence documentation to match

This halves steady-state **desktop** presence `SET` + `PUBLISH` traffic
while retaining tolerance for two missed heartbeats. Mobile already uses
a 60-second heartbeat, so the fleet-wide reduction depends on desktop's
share of connected clients.

## Rollout order

Deploy the relay TTL increase before shipping the desktop heartbeat
change. Old desktop + new relay is safe; new desktop + old relay leaves
only a 90-second TTL on a 60-second cadence and can flap after one
missed heartbeat.

## Verification

At initial live-test commit `00816e233b187bc5ba12c667d675ed050a8cc1c9`:

- isolated clean-room relay built from the exact SHA against fresh
Postgres, Redis, and MinIO
- live Redis `MONITOR` observed kind-20001 writes as `SET ... EX 180`,
global `PUBLISH`, and clean-disconnect / explicit-offline `DEL`
- normal workflows passed: channel create/update/archive/unarchive;
message send/get/reply/thread/search; archived-channel write rejection
and resumed write after unarchive

At follow-up commit `bf38a8c5c96f196ff8ee46e48d4141ee7811f186`:

- `pnpm -C desktop test` — 3829 passed
- `pnpm -C desktop typecheck`
- `cargo test -p buzz-pubsub` — 24 passed, 11 Redis-dependent tests
ignored
- mutation probes fail when the server TTL changes to `999999` or the
desktop heartbeat changes back to 30 seconds
- `git diff --check`

The pre-push suite's relevant checks passed, but its unrelated Tauri
clippy step fails on current `origin/main`:
`desktop/src-tauri/src/linux_media.rs` has three dead-code warnings on
macOS. This PR does not modify that file, so the branch was pushed after
independently running the suites above.

## Buzz context

Originating channel: `buzz-redis-cluster-mode`
(`f4e36d32-afdb-447f-8c87-ab003e069d18`)

---------

Signed-off-by: npub1t2tgm7d8f995uqvmnm8h88sg3wnpp9a5xysjf6dg3tjmgt3ltulqdp8ehr <5a968df9a7494b4e019b9ecf739e088ba61097b4312124e9a88ae5b42e3f5f3e@buzz.block.builderlab.xyz>
Co-authored-by: npub1t2tgm7d8f995uqvmnm8h88sg3wnpp9a5xysjf6dg3tjmgt3ltulqdp8ehr <5a968df9a7494b4e019b9ecf739e088ba61097b4312124e9a88ae5b42e3f5f3e@buzz.block.builderlab.xyz>

ARCHITECTURE.md

@@ -447,7 +447,7 @@ The subscriber uses a **dedicated** `redis::aio::PubSub` connection — not from
 
 **Reconnection:** exponential backoff 1s → 30s (`backoff_secs * 2`). Backoff resets to 1s only after a clean stream end, not on each reconnect attempt.
 
-**Presence:** `SET buzz:presence:{pubkey_hex} {status} EX 90` — 90-second TTL (3× the 30-second heartbeat interval). Single missed heartbeat does not cause presence flap.
+**Presence:** `SET buzz:presence:{pubkey_hex} {status} EX 180` — 180-second TTL (3× the 60-second heartbeat interval). Single missed heartbeat does not cause presence flap.
 
 **Typing indicators:**
 ```
@@ -797,7 +797,7 @@ Docker Compose provides the full local development stack. All services include h
 | Pattern | Type | TTL | Purpose |
 |---------|------|-----|---------|
 | `buzz:channel:{uuid}` | Pub/Sub channel | — | Event fan-out (single-community form; shared multi-community Redis must use `buzz:{community}:channel:{uuid}` or equivalent) |
-| `buzz:presence:{pubkey_hex}` | String | 90s | Online/away status (single-community form; shared multi-community Redis must scope by community) |
+| `buzz:presence:{pubkey_hex}` | String | 180s | Online/away status (single-community form; shared multi-community Redis must scope by community) |
 | `buzz:typing:{channel_uuid}` | Sorted Set | 60s | Active typers (5s window; shared multi-community Redis must scope by community) |
 
 ### Full-Text Search (Postgres FTS)