Function apply_progress_bindings 

pub fn apply_progress_bindings(
    store: Res<'_, PropertyStore>,
    q: Query<'_, '_, (&BindValue, &mut ProgressBar, Option<&mut A11yValue>)>,
    new_binds: Query<'_, '_, (), Added<BindValue>>,
)

Pull bind-value signal writes into ProgressBar::value. Same dirty-gated shape as lumen_core::signals::apply_value_bindings (which targets sliders - progress deliberately does not carry a SliderValue, or it would inherit wheel / click / drag mutation), and installed with the same ordering, after every store writer, so a write’s one-tick dirty flag is still set when this reads it.