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/pages/doctor.dart

@@ -481,7 +481,7 @@ class _PathRow extends StatelessWidget {
 
 /// Daemon control affordances: Restart, Apply update, Stop.
 /// Each shells out to the `fai` binary (resolved via PATH or
-/// `~/.fai/bin/chain`). Studio is the GUI shell; the binary owns
+/// `~/.chain/bin/chain`). Studio is the GUI shell; the binary owns
 /// the supervisor logic so the daemon and CLI stay in lockstep.
 class _DaemonActionsCard extends StatefulWidget {
   @override
@@ -817,7 +817,7 @@ class _ServicesPanel extends StatelessWidget {
     final l = AppLocalizations.of(context)!;
     if (snapshot.services.isEmpty) {
       // Wrap on narrow windows so the mono-spaced hint
-      // (`add to ~/.fai/config.yaml under services:`) does not
+      // (`add to ~/.chain/config.yaml under services:`) does not
       // overflow horizontally past the card's right edge.
       return FaiCard(
         child: Wrap(

lib/pages/store.dart

@@ -57,7 +57,7 @@ class _StorePageState extends State<StorePage> {
   bool _todayDismissed = false;
 
   /// The carousel of stories rendered in the hero. When an
-  /// operator-accepted story exists at `~/.fai/today/active.yaml`,
+  /// operator-accepted story exists at `~/.chain/today/active.yaml`,
   /// it is the only entry (carousel collapses to a single
   /// slide). Otherwise the curated fallback list rotates.
   late final List<TodayStoryData> _todayStories = (() {
@@ -2991,7 +2991,7 @@ class _ScreenshotPlaceholder extends StatelessWidget {
 }
 
 /// Compiled-in fallback stories shown when
-/// `~/.fai/today/active.yaml` is absent or fails schema
+/// `~/.chain/today/active.yaml` is absent or fails schema
 /// validation. Operator can override at any time without
 /// recompiling Studio — see docs/today-pipeline.md. When the
 /// operator accepts a story, that single story becomes the
@@ -3082,9 +3082,9 @@ const List<TodayStoryData> _kFallbackTodayStories = <TodayStoryData>[
     titleEn: 'Tamper-evident hash chain — built in',
     titleDe: 'Manipulationssicher per Hash-Kette — eingebaut',
     bodyEn:
-        'Every flow run, every install, every approval lands in ~/.fai/audit/ as a hash-chained event log. Any later edit invalidates the chain. CRA-ready out of the box — no compliance product to buy on top.',
+        'Every flow run, every install, every approval lands in ~/.chain/audit/ as a hash-chained event log. Any later edit invalidates the chain. CRA-ready out of the box — no compliance product to buy on top.',
     bodyDe:
-        'Jeder Flow-Lauf, jede Installation, jede Freigabe landet in ~/.fai/audit/ als hash-verkettetes Event-Log. Jede spätere Änderung bricht die Kette. CRA-tauglich von Haus aus — kein Compliance-Produkt zum Aufkaufen nötig.',
+        'Jeder Flow-Lauf, jede Installation, jede Freigabe landet in ~/.chain/audit/ als hash-verkettetes Event-Log. Jede spätere Änderung bricht die Kette. CRA-tauglich von Haus aus — kein Compliance-Produkt zum Aufkaufen nötig.',
     ctaLabelEn: '',
     ctaLabelDe: '',
     icon: Icons.timeline_outlined,
@@ -3110,9 +3110,9 @@ const List<TodayStoryData> _kFallbackTodayStories = <TodayStoryData>[
     titleEn: 'Build a module in a single Rust file',
     titleDe: 'Ein Modul in einer einzigen Rust-Datei bauen',
     bodyEn:
-        'fai-module-sdk gives you a #[fai::module] macro and a Cargo target. Declare inputs / outputs in module.yaml, write the function, cargo build, drop the wasm in ~/.fai/modules. The hub picks it up at next list. Polyglot SDKs follow in Phase 1.',
+        'fai-module-sdk gives you a #[fai::module] macro and a Cargo target. Declare inputs / outputs in module.yaml, write the function, cargo build, drop the wasm in ~/.chain/modules. The hub picks it up at next list. Polyglot SDKs follow in Phase 1.',
     bodyDe:
-        'fai-module-sdk liefert ein #[fai::module]-Makro und ein Cargo-Target. Inputs / Outputs in module.yaml deklarieren, Funktion schreiben, cargo build, das wasm in ~/.fai/modules legen. Der Hub erkennt es beim nächsten Listing. Polyglott-SDKs folgen in Phase 1.',
+        'fai-module-sdk liefert ein #[fai::module]-Makro und ein Cargo-Target. Inputs / Outputs in module.yaml deklarieren, Funktion schreiben, cargo build, das wasm in ~/.chain/modules legen. Der Hub erkennt es beim nächsten Listing. Polyglott-SDKs folgen in Phase 1.',
     ctaLabelEn: '',
     ctaLabelDe: '',
     icon: Icons.code_outlined,

lib/pages/welcome.dart

@@ -1123,7 +1123,7 @@ class _DocReaderError {
   });
 
   String get forgejoUrl =>
-      'https://git.flemming.ai/fai/platform/src/branch/main/docs/architecture/$slug.md';
+      'https://git.flemming.ai/fai/chain/src/branch/main/docs/architecture/$slug.md';
 
   /// Localized, operator-facing failure body. Use this for any
   /// on-screen rendering; [toString] stays English for logs.