Inject request object if root page wants it (zauberzeug#5263)

### Motivation

Root page functions should support the same parameter injection patterns
as regular `@ui.page()` decorated functions for consistency and to
provide access to request details (headers, cookies, URL components,
etc.).

### Implementation

Reuse existing page._wrap() infrastructure rather than duplicating
logic. The wrapped page function already inspects signatures and injects
request when present, so we simply avoid conflicting with it.

There currently is no proper documentation location for root page
specifics. Therefor I decided to not do this in this PR (simplifies
review) and ideally add another PR later to do comprehensive
documentation for root page.

### Progress

- [x] I chose a meaningful title that completes the sentence: "If
applied, this PR will..."
- [x] The implementation is complete.
- [x] Pytests have been added.
- [x] Documentation will be added in a separate PR.

---------

Co-authored-by: Falko Schindler <[email protected]>

Author: rodja

nicegui/nicegui.py

@@ -166,7 +166,7 @@ async def _exception_handler_404(request: Request, exception: Exception) -> Resp
                 param.annotation,
             )
             for name, param in inspect.signature(root).parameters.items()
-            if name in request.query_params
+            if name in request.query_params and name != 'request'
         }
         return await page('')._wrap(root)(request=request, **kwargs)  # pylint: disable=protected-access
     log.warning(f'{request.url} not found')

tests/test_root_page.py

@@ -33,3 +33,20 @@ def root(x: int = 0):
 
     screen.open('/?x=42')
     screen.should_contain('x = 42')
+
+
+def test_root_page_with_request_injection(screen: Screen):
+    from fastapi import Request
+
+    def root(request: Request):
+        ui.label(f'path: {request.url.path}')
+        ui.label(f'name: {request.query_params.get("name", "unknown")}')
+
+    screen.ui_run_kwargs['root'] = root
+    screen.open('/')
+    screen.should_contain('path: /')
+    screen.should_contain('name: unknown')
+
+    screen.open('/?name=test')
+    screen.should_contain('path: /')
+    screen.should_contain('name: test')