When we change ViewSheet.SheetNumber values change but Project Browser needs to be refreshed to show new values.
This snippet will Hide and Show ProjectBrowser and therefore update shown values.
from Autodesk.Revit.UI import DockablePanes, DockablePane
project_browser_id = DockablePanes.BuiltInDockablePanes.ProjectBrowser
project_browser = DockablePane(project_browser_id)
project_browser.Hide()
project_browser.Show()