fix(studio): chain config dir + spawn path + doc URLs

Track the platform rename: the hub spawn path is now ~/.chain/bin/chain
(was ~/.fai/bin/fai.exe on Windows — both dir and binary were stale, so
Studio could not launch the hub after the config-dir rename), the
~/.fai/* help strings become ~/.chain/*, FAI_REGISTRY_TOKEN ->
CHAIN_REGISTRY_TOKEN, and the two in-app doc URLs point at the public
fai/chain repo (fai/platform was renamed to the private fai/chain-private).
The .fai module bundle extension is left unchanged (format phase).
flutter analyze: no issues.

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

lib/data/registry_token.dart

@@ -2,8 +2,8 @@ import 'dart:io';
 import 'package:path/path.dart' as p;
 
 /// Operator-managed registry auth token, kept at
-/// `~/.fai/registry-token` (mode 0600 on Unix). The hub reads
-/// this file at install time when `FAI_REGISTRY_TOKEN` is unset
+/// `~/.chain/registry-token` (mode 0600 on Unix). The hub reads
+/// this file at install time when `CHAIN_REGISTRY_TOKEN` is unset
 /// — see `download_to_temp` in `crates/fai_hub/src/lib.rs`.
 ///
 /// Studio writes the file directly so a fresh install never
@@ -40,7 +40,7 @@ class RegistryToken {
     return trimmed.isEmpty ? null : trimmed.length;
   }
 
-  /// Persist [token] to disk, creating `~/.fai/` if needed.
+  /// Persist [token] to disk, creating `~/.chain/` if needed.
   /// On Unix the file is chmod-ed to 0600 (owner read/write
   /// only). On Windows the default user-ACL is left alone —
   /// best-effort, no PowerShell handshake.