The most usual Russian unit awards were :
--- permission to play the "Grenadier March"
--- award of musical instruments, typically a pair of silver trumpets with Saint-George ribbons
--- award of Saint-George flags
--- award of "for excellence" shako badges
--- the naming of a member of the Russian imperial family and/or an allied foreign head of state as the unit's "(honorary) commander in chief".
Most of the above are covered here : link
As to unit "promotions", while the selection of the units to promote seems to be based largely on merit, the decision to increase the number of grenadier or guards units seems at least in part administrative.
Russian units promoted to "Grenadiers" 1787 through 1816
● 1790 Kherson and Astrakhan Infantry promoted to Grenadiers
● 1795 Caucasus Infantry promoted to Grenadiers
● 1811 Graf Arakcheev's Musketeers promoted to Grenadiers
● 1813 Kexholm and Pernau Infantry promoted to Grenadiers
● 1814 1st, 3rd, 8th, 14th, 26th and 29th Jäger promoted to Grenadier Jäger ("Carabiniers" from 1815)
● 1816 7th Jäger promoted to Carabiniers
In 1796, the "Gatchina Force", the former Tsarevich's demonstration units, were taken into the Guard :
--- 3 squadrons of armored Gendarmes to the Horse Guards
--- 3 squadrons of Dragoons to the Horse Guards
--- 2 squadrons of Hussars to the Life-Hussars
--- 2 squadrons of Don Cossacks to the Life-Cossacks
--- 6 battalions of heavy infantry to expand the existing regiments
--- 1 batallion Jäger to the Life-Guard Jäger
--- 3 Foot and 1 Horse Artillery companies to the Life-Guard Artillery
Russian units promoted to "Life" or "Life-Guards" 1787 through 1816
● 1796 His Highness the Tsarevich's Cuirassiers promoted to His Majesty the Emperor's Life-Cuirassiers
● 1798 the Life-Hussars and Life-Cossacks promoted to Life-Guards
● 1808 the Imperial Militia promoted to Life-Guards
● 1809 His Highness the Tsarevich's Lancers promoted to Life-Guards
● 1813 the Life-Grenadiers, Pavlovsk Grenadiers and His Majesty the Emperor's Life-Cuirassiers promoted to Life-Guards
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I would agree that the "Moskovets" were exceptionally steady, even among the Russian infantry. They took 50%+ casualties in several engagements without wavering or slackening.
Moscow Infantry regiment / Московскій Пѣхотный полкъ
--- founded in 1699 : one of the most senior infantry regiments
--- 1791 Kuban campaign, storm of Anapa
--- 1796 Persian campaign, capture of Derbent
--- 1803 Lieutenant General Dokhturov appointed "commander in chief"
--- 1805 distinguished at Dürenstein and in the retreat from Austerlitz
--- 1807 distinguished at Eylau / Lomiten, Heilsberg and Friedland
--- ~1810 issued Russian Model 1808 muskets
--- 1812 1st & 3rd battalions : Smolensk, Borodino (the regiment's commander, Colonel Fyodor Fyodorovich Monakhtin, was mortally wounded), Tarutino and Maloyaroslavets / 2nd battalion : defense of Dinaburg and battles of Polotsk)
--- 1813 sieges of Glogau, Pillau, Danzig, Wittenberg and Kassel / battle of the Katzbach
--- 1814 distinguished at Brienne-le-Chateau / La Rothière, La Ferté-sous-Jouarre, Montmiral and Craon
--- 1815 awarded 2 Saint George trumpets