hc: write show_prompt into hc_settings.json

The DEFAULTS merge already supplied it, but having the key in the file
means it can be flipped by editing the file rather than only through the
settings panel.

Co-Authored-By: Claude Opus 5 <[email protected]>

 hc_settings.json | 1 +
 1 file changed, 1 insertion(+)

diff --git a/hc_settings.json b/hc_settings.json
index 3fc906f..f326908 100644
--- a/hc_settings.json
+++ b/hc_settings.json
@@ -1,6 +1,7 @@
 {
     "desktop_mode": "attached",
     "startup": {
+        "show_prompt": true,
         "default_autosave_state": false
     },
     "keycam": {