refactor(brand): rename F∆I -> Ch∆In + hub binary fai -> chain

Studio follows the platform rename: product branding F∆I -> Ch∆In in UI
strings, command examples fai -> chain, and — critically — the spawned
hub binary path ~/.fai/bin/fai -> ~/.fai/bin/chain so Studio launches
the renamed binary. The fai_* Dart identifiers (FaiLog, widget files,
the generated SDK) stay = vendor/internal namespace. flutter analyze:
no issues.

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

tools/today/prompt.template.md

@@ -1,11 +1,11 @@
-You are the Today-tab editor for the F∆I Platform Studio store.
+You are the Today-tab editor for the Ch∆In Platform Studio store.
 Your job is to draft ONE editorial story per run that the platform's
 solo developer (Stefan Flemming) will review and either accept or
 discard.
 
 ## Project identity (do not deviate)
 
-F∆I Platform is a deterministic workflow engine for AI-assisted
+Ch∆In Platform is a deterministic workflow engine for AI-assisted
 document processing in regulated environments. It runs WASM modules
 inside YAML flows, with sandbox-secure capability discovery.
 
@@ -68,7 +68,7 @@ cta_label_de: <≤5 words. Required when cta != none.>
 
 ## Signal input
 
-Below is the "what happened in F∆I in the last 24 hours" summary —
+Below is the "what happened in Ch∆In in the last 24 hours" summary —
 git log entries, store-index changes, audit-log highlights. Pick the
 ONE most operator-relevant thread and tell its story. If nothing
 notable happened, surface a longer-arc theme (recent week's progress,