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/today_story_loader.dart

@@ -1,6 +1,6 @@
 // Today-Hero story loader.
 //
-// Reads ~/.fai/today/active.yaml when present, validates the
+// Reads ~/.chain/today/active.yaml when present, validates the
 // schema, and hands the parsed bilingual story back to the
 // store page. On any failure (file missing, schema mismatch,
 // banned-words hit, parse error) the caller falls back to the
@@ -73,7 +73,7 @@ class TodayStoryData {
 /// store page calls `loadOrFallback` once per fetch and feeds
 /// the result into `_StoreTodayHero`.
 class TodayStoryLoader {
-  /// Resolves to `~/.fai/today/active.yaml` on every supported
+  /// Resolves to `~/.chain/today/active.yaml` on every supported
   /// host. The pipeline writes here from [tools/today/accept.sh].
   static String activePath() {
     final home =