I'd like to see Russian ruler who is neither Catherine, nor Peter, nor any Soviet leader. Just so we could get out of the eternal pendulum between these two, with the occasional nod to USSR. 18th century is wildly overrepresented era of Russian history anyway.
I'd love to see Russian civ built around earlier eras than westernized 18th century, with leaders such as Dmitryi Donsky, Alexander Nevski, Ivan III the Great, some good 17th century tsar, but not Ivan Grozny as he's that one old Russian ruler who is overrepresented in culture, no doubt because of him fitting the bill of the "Russian despot".
Then, you design Russian civ which does not contain any beaten to death trope such as "much land bonus" or "many soldiers bonus" or especially any nonsensical bonuses related to winter or cold climate, and now we can have something interesting. Bonus points for the unique unit not being streltsy or cossacks. Bonus points from making Russian civ explicitly less exttemely imperialist than the usual depiction.
Honestly my dream would be Russian civilization with Novogrod as a capital, Nevsky as a leader, mighty mercantile and industry bonuses, and defensive focus - it would just gloriously subvert every boring convention imaginable, while still being perfectly historically accurate and depicting legitimately great aspects of Russian history.
Just to point out, while Ivan IV has been the subject of considerable popular media attention (by my count, at least 3 movies and a television series in Russia alone), he is a good candidate for a Counter-Popular Image Leader for Russia. In addition to his far too well known despotic tendencies - which, frankly, were the Norm rather than the Exception in 15th - 16th century Europe - he also built the first printing plant in Moscow, penned dozens of essays and printed material himself, and had the "Saint Basil's" architecturally unique cathedral/Sobor built. You could easily and just as accurately make him more of a religious/scientific than a despotic militaristic Leader.
Now as to Unique Units.
As a military historian, I've run across numerous 'unique' attributes and units for military establishments, most of which have either been grossly misrepresented in Civ or ignored completely. Russia is no exception.
The Cossacks were enemies of Russia until they were brought under control, so if they have to be in the game (and they don't!) they should be a Unique Unit that Russia can get from 'Barbarians' nearby or from a City State (Zaporozhye or Krasnodar would be good candidates). The distinctive Cossack Unit was not a 19th century Cavalry equivalent, but light cavalry lancers of the 17th - 18th century at a time when the lance had completely fallen out of favor almost everywhere else.
Among the distinctive Russian 'methods and instruments of war' that could be really new Uniques:
1. Peter the Great's
Corps Volante - mounted infantry and dragoons that could out maneuver the enemy on horseback, then dismounted to fight with muskets.
2. mid-18th century Licornes or Unicornes - howitzers that could also fire directly with solid or explosive shot, a unique Field Cannon against either troops or buildings.
3. Kolkhoz Infantry. In the 1930s, the Soviet Army had several rifle divisions in the Far East that were 'cadre' (active duty) units labeled 'Kolkhoz' (abbreviation for 'Collective Farm'). Basically, they worked the farms while also training as soldiers, and they had enough farmworkers to create 3 rifle divisions out of them instantly if needed. A modern Infantry unit that also provides 'extra' Food and/or Production points.
4. M1902 Cannon 76.2mm. The French '75' of 1897 was the first and most famous early modern gun with a recoil mechanism, but the Russian M1902 came right after, was lighter, as accurate, and was improved and 'upgraded', unlike the French gun, right up to the end of WWII: the ZIS-3 76.2mm of 1942 was a direct descendant, and used as light artillery, antitank artillery, and divisional artillery until the end of the war.
5.
Shturmovik: The IL-2 attack aircraft, the first 'flying tank'. IF Civ VII gets air power right, or at least 1/3 right, this would be a better 'modern' Russian/Soviet UU than any ground unit: more
IL-2s were built than any other Soviet aircraft and they were used against every imaginable ground target within range, hitting enemy armor, headquarters, trucks, infantry positions, and many targets usually considered too dangerous to attack.
And by the way, although the image is indelibly attached to the Soviets, there was nothing particularly Soviet or Communist about the T-34: the engine was a copy of a French aircraft (diesel) engine, the chassis and suspension system from the American tank designer Christie, the main gun a development of the Imperial Russian M1902 76.2mm field cannon, and the sloped armor copied from a Dutch design of the 1930s.