refactor: rename package fai_client_sdk -> chain_client_sdk

The SDK belongs to the Ch∆In product, not the F∆I vendor namespace
(a future Brain client SDK would otherwise collide). Rename the Dart
package, entry library, test + example files. Also drop a private
project name from a doc comment. dart analyze: clean.

Dependents must update their dependency name + package: imports.

Signed-off-by: flemming-it <stefan.a.flemming@googlemail.com>

README.md

@@ -1,4 +1,4 @@
-# fai_client_sdk (Dart)
+# chain_client_sdk (Dart)
 
 gRPC client SDK for the Ch∆In hub. Used by F∆I Studio
 (Tier-2 generic GUI) and any Tier-3 Dart/Flutter domain app
@@ -9,10 +9,10 @@ One of the three SDK families documented in
 
   * `fai-module-sdk` (Rust) — flow modules
   * `fai-plugin-sdk` (Rust) — Studio plugins
-  * `fai_client_sdk`  (Dart) — clients ← this package
+  * `chain_client_sdk`  (Dart) — clients ← this package
 
 Dir / repo carries the `_dart` / `-dart` language suffix
-(`fai_client_sdk_dart` / `client-sdk-dart`); the Dart package
+(`chain_client_sdk_dart` / `client-sdk-dart`); the Dart package
 name itself does not (Dart-land doesn't need the suffix).
 
 > **Status (2026-05-05):** scaffold. Public surface (`HubClient`,
@@ -35,9 +35,9 @@ boilerplate. This package centralises that work:
 ## Layout
 
 ```
-fai_client_sdk_dart/
+chain_client_sdk_dart/
 ├── lib/
-│   ├── fai_client_sdk.dart        # Public API
+│   ├── chain_client_sdk.dart        # Public API
 │   └── src/
 │       ├── hub_client.dart        # Typed client wrapper
 │       ├── channel_factory_io.dart   # Native ClientChannel (HTTP/2)