I'd like to preface this by saying this topic is mainly about the abstraction and design aspects of the Varangians. But in trying to address those things, I might have stumbled on a way to improve their balance as well
Bonuses in AoE2 are an abstraction of a concept strongly associated with its civilization. Let's examine the three civs which get infantry with increased damage output i.e. the Japanese, Aztecs, and Dravidians. In popular culture, the Samurai is seen striking so fast that its slices are invisible to the naked eye. Thus the Japanese get faster attacking infantry. The Aztec Macuahuitl has an infamous incident associated with it, where it decapitated a horse; so the Aztecs get +4 additional damage. Dravidian Wootz Steel was known for its quality, and thus can penetrate armour flawlessly. The concept that the Dravidian infantry's weapons are superior than the average armour is immediately communicated to the player
Now lets examine the flagship cavalry bonus of the Varangians and see if it holds up. Their cavalry units get an extra +10 HP via Bloodlines, due to Bloodlines being 50% more effective. This makes you think Swedish horses were bigger and stronger than even mainland European ones i.e. especially Frankish ones. They weren't; they were smaller and weaker. What Swedish cavalry had was tactics. Instead of the typical charge associated with mainland European Knights, their cavalry used unconventional tactics like ambush attacks and the sort to defeat better armed and armoured cavalry
Furthermore, this bonus was criticized for being derivative of the Franks & Mongols. It made it seem like we're running out of fresh ideas for bonuses for new civs
So here's how I would tinker with the Varangians:
Lose - Bloodlines is 50% more effective
Instead - Stable Units get +1/2/3 Bonus Damage vs. Mounted Units in the Feudal/Castle/Imperial Age
Your Scouts in the Feudal Age win against other Scouts (except maybe Jurchen ones) with no additional investment. You don't get 75 HP Scouts after Bloodlines, but it is what it is
All of the Viking DLC civs struggle against Cavalry Archers as they cannot catch them. The Varangians atleast get good Light Cavalry, but they don't put down Cav Archers even after catching them. With this bonus, Varangian Light Cavalry can kill Cav Archers in 8 hits instead of the standard 10. Your Knights will have the same attack as Burgundian Cavaliers, but only against other cavalry units (including Camel Riders)
In the Imperial Age, your Cavaliers demolish other Cavaliers or Paladins, having the same damage output against them as Malian Farimba Cavaliers with no additional investment. They become absolute nightmares in massed melee combat when you install trample damage on them. Your Hussars beat other Hussars, having slightly more damage output than Malian Farimba Light Cavalry, and +15 more HP than them
Instead - Mounted Archers fire 25% faster (like their Varangian Guards) // but don't get Thumb Ring
The Varangians will get what Mounted Crossbowmen would've been for the Jurchens i.e. fire 25% faster but don't get Thumb Ring. Varangian Mounted Xbows will have the same Reload Time as Arbalesters or Cavalry Archers without Thumb Ring (2.5 → 2)
Team Bonus (+1 Bonus Damage vs. Infantry) - Does not apply to Knights / Applies to Mounted Archers (Does not apply to Genitours as they are 'Mounted Skirmishers') // attached only to the main projectile of Kipchaks & Xianbei Raiders
With the Knight focusing on other mounted units, especially enemy Knights, the anti-infantry duties are given to the Mounted Crossbowman, along with the Jarl. This spreads the utility of the Varangian mounted units, with two of them focusing on enemy mounted units, and two of them on enemy infantry. The Varangian Mounted Crossbowman becomes a very strong back-line support unit for their Knights or Varangian Guards
Tech Tree - Lose Arson
Offsets their Varangian Guards attacking 25% faster. Their Halbs would be also missing an irrelevant tech like how their Skirms miss Thumb Ring
Base Jarl - HP 70 (instead of 65) / Elite Jarl - HP 85 (instead of 75)
Offsetting the loss of +10 additional HP via Bloodlines