Fix the rail picker going nameless — my own regression from the row rework

Giving each project row a widget left the QListWidgetItem with no text, and
project_choices() read exactly that. So the rail's picker listed every project
as a bare "📁 " with nothing after it, and the more projects there were the more
identical blanks you got. Reported after creating a second one.

Setting the text back on the item is not the fix: with a transparent row widget
on top, the name paints twice, one string ghosting the other — visible in a
render. project_choices() now reads list_projects(), the same source the list
is built from, so the picker no longer depends on how a row happens to be drawn.

check_project_screen creates a project and requires project_choices() to return
non-empty names and the picker to show each of them. Pointing it back at
item.text() fails it.

22/22 checkers pass.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

tools/check_project_screen.py

@@ -103,6 +103,26 @@ def main() -> int:
             fails.append(f"thieu nhan {label!r}")
     print(f"nhan form: {want}")
 
+    # 5. the rail's picker must name the projects. It reads project_choices(),
+    #    which used to read item.text() — and when rows became widgets the item
+    #    text went empty, so every entry showed as a bare folder glyph. Creating
+    #    a project is when a user notices, so create one here.
+    before = [n for n, _pid in w.project_choices()]
+    w._create()
+    app.processEvents()
+    choices = w.project_choices()
+    picker = [win.nav_project.itemText(i) for i in range(win.nav_project.count())]
+    print(f"project_choices: {[n for n, _p in choices][:4]}")
+    print(f"picker hien thi: {picker[:4]}")
+    if any(not name.strip() for name, _pid in choices):
+        fails.append("project_choices tra ve ten rong")
+    if len(choices) <= len(before):
+        fails.append("tao project moi khong vao danh sach")
+    for name, _pid in choices:
+        if not any(name in text for text in picker):
+            fails.append(f"picker khong hien ten {name!r}")
+            break
+
     print()
     for f in fails:
         print("FAIL  " + f)