feat(run): tool-aware model picker and run panel labels for codex lanes

Model dropdown now shows curated Claude vs Codex models per lane's tool,
and the run panel title/subtitle/binary-missing text switch between
"Chạy Claude"/"Chạy Codex" accordingly.

client/src/lib/api.ts

@@ -2719,18 +2719,20 @@ export const RUN_EFFORT_CHOICES: EffortChoice[] = [
 // configured default and the rest map to concrete `--model` values.
 export const RUN_MODEL_CHOICES: ModelChoice[] = [
   { id: "", label: "Inherit from settings", hint: "Use whatever your settings.json model is" },
-  {
-    id: "claude-opus-4-8[1m]",
-    label: "Opus 4.8 (1M context)",
-    hint: "Highest capability, 1M token window",
-  },
-  {
-    id: "claude-opus-4-7[1m]",
-    label: "Opus 4.7 (1M context)",
-    hint: "Previous Opus, 1M token window",
-  },
-  { id: "sonnet", label: "Sonnet 4.6", hint: "Balanced capability and speed" },
-  { id: "haiku", label: "Haiku 4.5", hint: "Fastest, lightest" },
+  { id: "claude-opus-5", label: "Opus 5", hint: "Highest capability" },
+  { id: "claude-sonnet-5", label: "Sonnet 5", hint: "Balanced capability and speed" },
+  { id: "claude-fable-5", label: "Fable 5", hint: "Fast output, same capability tier as Opus" },
+  { id: "claude-haiku-4-5-20251001", label: "Haiku 4.5", hint: "Fastest, lightest" },
+];
+
+// Curated model list for Codex lanes - same shape as RUN_MODEL_CHOICES, sent
+// via `codex -m`. "" inherits Codex's own configured default.
+export const RUN_MODEL_CHOICES_CODEX: ModelChoice[] = [
+  { id: "", label: "Inherit from settings", hint: "Use whatever your Codex config model is" },
+  { id: "gpt-5.6-sol", label: "GPT-5.6 Sol", hint: "Highest capability" },
+  { id: "gpt-5.6-terra", label: "GPT-5.6 Terra", hint: "Balanced capability and speed" },
+  { id: "gpt-5.6-luna", label: "GPT-5.6 Luna", hint: "Fastest, lightest" },
+  { id: "gpt-5.5", label: "GPT-5.5", hint: "Previous generation" },
 ];
 
 /** Result of a transcript import run - returned by `api.import.rescan`,