Follow the active theme in T3 Code

T3 Code reads themes an environment publishes into its state directory, so
a generated t3code.json carries the palette the same way claude.json and
vscode-theme.json already do, and omarchy-theme-set-t3code republishes it
on every theme change for the app to pick up live.

The template overrides only the roles a theme actually designs -- terminal
and code surfaces, text on canvas, borders, selection -- and leaves muted
text, placeholders, and status foregrounds to T3 Code, which contrast-solves
them against whatever canvas it is given. Overriding those directly cost
readability on light themes: White fell to 1.0:1 on placeholder text.

Installing from the menu now routes through omarchy-install-ai-t3-code so a
fresh install publishes the current palette and opens wearing it.

default/themed/t3code.json.tpl

@@ -0,0 +1,36 @@
+{
+  "name": "Omarchy",
+  "appearance": "{{ mode }}",
+  "canvas": "{{ background }}",
+  "accent": "{{ accent }}",
+  "colors": {
+    "chrome": "{{ background }}",
+    "toolbar": "{{ background }}",
+    "toolbarForeground": "{{ foreground }}",
+    "toolbarBorder": "{{ muted }}",
+
+    "text": "{{ foreground }}",
+    "border": "{{ muted }}",
+    "focus": "{{ accent }}",
+
+    "sidebar": "{{ dark_background }}",
+    "sidebarForeground": "{{ foreground }}",
+    "sidebarBorder": "{{ muted }}",
+    "sidebarRowHover": "{{ mix dark_background foreground 6% }}",
+    "sidebarRowActive": "{{ mix dark_background accent 18% }}",
+    "sidebarRowSelected": "{{ selection }}",
+
+    "error": "{{ mix red foreground 35% }}",
+    "warning": "{{ mix yellow foreground 35% }}",
+
+    "codeBackground": "{{ dark_background }}",
+    "codeForeground": "{{ foreground }}",
+
+    "terminalBackground": "{{ background }}",
+    "terminalForeground": "{{ foreground }}",
+    "terminalCursor": "{{ bright_foreground }}",
+    "terminalSelection": "{{ selection }}",
+    "terminalScrollbar": "{{ muted }}",
+    "terminalScrollbarHover": "{{ dark_foreground }}"
+  }
+}