Sync API reference from eigen-server

CONTRIBUTING.md

@@ -145,7 +145,7 @@ verify the `latest` link on `reference/dart.md`.
 ## Documentation versions
 
 The site is versioned on the **engine's release line**. Pre-1.0 that is the
-minor, so `0.2.x` is one line and `0.3.0` starts the next. The label lives in
+minor, so `0.3.x` is one line and `0.4.0` starts the next. The label lives in
 `docusaurus.config.ts` under `versions.current.label`, and
 `pnpm check-docs-version` asserts it against `info.version` in the committed
 `api/openapi.json`. CI runs that check on every pull request.
@@ -160,18 +160,25 @@ between two answers:
 **Freeze the old line**, the answer whenever a reader could still be running it:
 
 ```bash
-pnpm docusaurus docs:version 0.2.x   # the line being frozen, not the new one
+pnpm docusaurus docs:version 0.3.x   # the line being frozen, not the new one
 ```
 
-That snapshots `docs/` into `versioned_docs/version-0.2.x/` at `/docs/0.2.x/*`,
+That snapshots `docs/` into `versioned_docs/version-0.3.x/` at `/docs/0.3.x/*`,
 and `docs/` becomes the new line at `/docs/*`. Then set
 `versions.current.label` to the new line. The generated reference freezes with
 everything else, which is what you want, since `sync-api` only ever writes to
 `docs/`, so no part of that pipeline knows versions exist.
 
 **Relabel in place**, only when the old line was never published, or nobody can
-still be on it. Set `versions.current.label` and change nothing else. That is
-what happened at `0.2.x`: the site's first public deploy already described it.
+still be on it. Set `versions.current.label` and change nothing else. Both
+crossings so far took this answer, and the second one is the useful precedent
+because a cut was arguable: `0.2.x` was published and `eigen_flutter` 0.3.x was
+on pub.dev pinned to it, but the engine had no adopters to strand, and the
+release that crossed the line edited the game object's init migration in place,
+so a `0.2.x` game's local state did not survive the upgrade regardless. A frozen
+`0.2.x` line would have kept describing a wire no engine can speak, which is
+worse than not having it. (`0.1.x` was simpler: the site's first public deploy
+already described `0.2.x`, so no `0.1.x` page was ever reachable.)
 
 Freezing is not free. A cut copies all of `docs/`, and most of this site by
 volume is the generated TypeScript and HTTP reference, so each frozen line