I’d actually been of the (somewhat uninformed opinion) that Austrian grenadier battalions likely didn’t carry colors as they’d have been withheld by the parent battalions.
Russian converged grenadier battalions 1810-1815 were of the same basic model and they did not carry colors. The French converged elites (with a notable exception) were of a different model in that they were generally converged in the field and so would not have colors available but were significantly different since they weren’t formed for a campaign or war time. The grenadier division of 1805 did have colors but not French flags and not Eagles. The Prussian converged grenadier battalions (early war 1805-1807) did not carry colors either as they were left with the parent battalions.
So that was my working presumption.