perf: benchmark and optimize large-doc write and sync paths

[marcus-pousette]

This PR improves large-doc write and sync performance and adds benchmark coverage to measure those paths repeatably. The main runtime work is in the Postgres backend, with supporting benchmark instrumentation in the playground and benchmark runners.

Runtime changes

• add a Postgres-side cached replica counter path for local-op creation
  • treecrdt_replica_meta stores per-replica max counters
• add a seeded core construction path used by the Postgres local-op flow

Benchmark and test support

• add hot-write benchmarks for large existing docs: payload edits, sibling inserts, and move cases
• add reusable large-doc fixture setup for Postgres-backed runs
• keep @treecrdt/postgres-napi runtime-only and move fixture helpers under @treecrdt/postgres-napi/testing
• add playground live-write instrumentation for measuring remote writes on preseeded docs
• make read-only sync benches reuse matching seeded trees across reruns by default
• allow dedicated environments to prime remote fixtures directly with --postgres-url

Representative results

• remote partial-tree first-view on eu.sync.emhub.net
  • 10k structure-only: 266ms
  • 10k payload subtree: 242ms
  • 100k payload subtree: 210ms to 227ms
• public regional live-write
  • eu.sync.emhub.net: 189.9ms
  • us.sync.emhub.net: 241.3ms
  • sync.emhub.net: 254.8ms
• hot writes on existing 1m trees
  • Postgres N-API: payload edit 1.8ms, insert sibling 3.5ms, move leaf 47.7ms
  • sqlite-node file: payload edit 0.82ms, insert sibling 1.23ms, move leaf 2.20ms
  • sqlite-node memory: payload edit 0.13ms, insert sibling 0.23ms, move leaf 0.81ms

Not in scope here: public-host 1m seeding and remote re-sync results.

[github-actions]

Benchmarks

Triggered by workflow_dispatch (default) - Run: https://github.com/cybersemics/treecrdt/actions/runs/23849500797
Suite: high-value default (default)
Base: sync/doc-discovery-contract (69c02a2) - Head: sync/hot-write-benchmarks (c5c752e)
Compared entries: 8 - Improved: 2 - Regressed: 0

Impl	Storage	Workload	Base ops/s	Head ops/s	Δ ops/s	Base p50 ms	Head p50 ms	Δ p50	Status
postgres-napi	postgres	hot-write-insert-sibling-fanout10-100000-warm2-repeat10	-	9.22	-	-	108.49	-	✅
postgres-napi	postgres	hot-write-payload-edit-fanout10-100000-warm2-repeat10	-	18.30	-	-	54.64	-	✅
sqlite-node	file	hot-write-insert-sibling-fanout10-100000-warm2-repeat10	-	502.51	-	-	1.99	-	✅
sqlite-node	file	hot-write-payload-edit-fanout10-100000-warm2-repeat10	-	584.41	-	-	1.71	-	✅
sqlite-node	file	sync-balanced-children-payloads-cold-start-fanout10-100000-first-view	24.93	566.36	+2171.84%	842.37	37.08	-95.60%	🔴
sqlite-node	memory	hot-write-insert-sibling-fanout10-100000-warm2-repeat10	-	2175.54	-	-	0.46	-	✅
sqlite-node	memory	hot-write-payload-edit-fanout10-100000-warm2-repeat10	-	2428.30	-	-	0.41	-	✅
sqlite-node	memory	sync-balanced-children-payloads-cold-start-fanout10-100000-first-view	377.82	451.79	+19.58%	55.58	46.48	-16.37%	🟠

Status: ✅ <5% change | 🟡 5–10% | 🟠 10–30% | 🔴 >30%

Artifacts:

• base summary: bench-base/benchmarks/summary.json
• head summary: bench-head/benchmarks/summary.json

[marcus-pousette]

/bench