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(