fix(contract): the flush gate's internals are #-private — they are not doors

The 10.4.11 flush single-flight work added `startFlushLeader` and
`promoteQueuedFlush` as TypeScript `private` methods. `private` is erased at
compile time, so both still land on the prototype — and the contract manifest
emitter reads the surface the BUILD exposes, skipping only names that start with
an underscore. On the next regeneration both would have been emitted as contract
doors, obliging every engine implementing contract 1 to provide the flush gate's
own bookkeeping. A door is a promise; these are internals.

Converted to ECMAScript-private (`#`), which keeps them off the prototype
entirely, and the reason is recorded on both so the next internal is not written
as `private` by habit. `_runFlush` — the flush body itself — was already safe by
the emitter's underscore rule.

Verified: `npm run build && node scripts/emit-contract-manifest.mjs` then
`--check` green at 302 doors, with neither name present.

TWO MANIFEST NOTES, both deliberate and neither hidden:

1. The regenerated manifest gains `MetadataArrayTooLargeError`. The emitter
   lists every `*Error` export from brainyError.js, and that class is the write
   door's refusal for an over-bound metadata array (this branch's array-bound
   commit). It is a real addition to the engine's error surface, so the manifest
   is right to carry it — flagged here because it is a contract-surface change
   that the cut should accept knowingly, not a side effect that slipped in.

2. `armIdleFlushTimer` and `kickBackgroundFlush` are TypeScript `private` in
   src and ARE already in the committed manifest as doors — the same leak, one
   release older. They are left exactly as they are: removing a name the
   manifest already publishes is a contract deletion, not a hygiene fix, and it
   belongs to whoever owns contract 1 rather than to this branch.

docs/api-contract.json

@@ -1507,6 +1507,7 @@
     "BrainyError",
     "DerivedArtifactMissingError",
     "GraphIndexNotReadyError",
+    "MetadataArrayTooLargeError",
     "MetadataIndexNotReadyError",
     "MigrationInProgressError",
     "ProtectedArtifactError",