feat: add rust browser terminal prototype

README.md

@@ -0,0 +1,17 @@
+# BASE_PATH Demo
+
+Minimal Leptos SSR project that reuses a few components from `ui` to validate `SiteConfig::BASE_PATH`.
+
+The public app path is `/rustui`, while Leptos SSR routes are still declared as `/`, `/check`, and `/deep/nested`. The server strips `/rustui` before route matching, and the client router uses `/rustui` as its base.
+
+```bash
+cargo leptos watch
+```
+
+Then open:
+
+- `http://127.0.0.1:3100/rustui`
+- `http://127.0.0.1:3100/rustui/check`
+- `http://127.0.0.1:3100/rustui/deep/nested`
+
+Change `app_config/src/lib.rs` to test another base path.