Dialog for selecting projects can be replaced with a new one. - Replace Button that opens it. - Replace the dialog itself. - Use `<Listbox>` to render list. - Use [`<ProjectItem>`](#9223) to render project content inside the list, pass it to render function. <img width="1884" height="646" alt="Image" src="https://github.com/user-attachments/assets/e1894ce8-ad92-44f9-8db0-247934b62ed1" />