In the 8th/9th c. and parts of the 10th c. there's Norse-associated artifacts all over the waterways along the Volga trade routes, so the "forts" in "Gardar" - were probably held by some Scandinavian-heavy merchant/warrior caste.
There's a transition period where these sites are burned, the rebuilt as "Rus" sites - Nordic but with much more noticeable Slavic elements.
These sites are generally abandoned by the end of the century and all the action moves to nearby satellite towns instead. It's also the period where raids on the Caspian end, and Norse/Slav trade settlements in Bulgar lands get abandoned. People are coming not to trade but to tax, not to raid but to live. Nonetheless the Byzantine treaty texts has a lot of Scandiavian names, and few Slavic ones, as well as some of unknown origin. Scandinavians are present but some of them already have Slavic patronymics. This isn't assimilation no more than 12th c. Black Hats are assimilated, but it's an indication that they are taking on local customs.
By the 11th c. there are only two places where the Norse are present in any numbers: Ladoga (even had its own Jarl as a vassal of the Princes of Novgorod), and Kiev itself (serving in the Guard). These are all people with strong connections to Norway or more rarely Sweden who aren't destined to survive as a long-term native population. Those who do and enter Rus nobility in this period and later are basically Russian (Slavic names and all) within a generation or two.
So that's what happened IRL.
Here are your problems with "Norse" Gardariki:
The Russian Finnic peoples have a distinct agriculture and that is less efficient than what the Slavs bring. Norse agriculture is more cold-adapted and intermediate between the two. The Slavs colonised the Finnic lands most thoroughly within a few hundred years.
Slavs have assumed population advantage. The only way to beat the Slavs in the numbers game is to drain swamps and do other heavy infrastructure improvements. That's basically what German colonization of Slavic Europe is about.
The Norse, however, have no record of achieving anything much like that outside Denmark, and what Denmark had is less sophisticated what the Rus produced around Kiev.
Initially Nordic warrior elites were successful because of access to Frankish steel and better warband organisations, with east-Slavic organisations being more family based and their leadership more sacral than military. Once that is rectified (by importing the Rurikids, for example), there is no real advantage to having Norse warriors over Slavic warriors in your retinue or your militia.
In fact, Sweden struggled to get its act together in the organisational sense until the mid-13th c. and Norway only started heading that way in the 11th c.
The Rus (now pretty Slavic) managed to colonize and consolidate a huge territory in the meanwhile, and then break apart and form several regional centres each of which was individually a match for say, Sweden.
Nonetheless, Varangians remain useful to the princes of Rus through to the 12th c. in some capacity. Their kings were kin to the ruling dynasty, yes, but they also had a tradition of military adventuring, so it was easy to raise a large force quickly for long-distance campaigns. Vladimir and Yaroslav both relied heavily on them and that was pretty late.
However, somewhere in the 11th c. we start seeing a paradigm shift in warfare in Eastern Europe:
Polish national armies beat Varangian-heavy Russian forces on several occasions. Yaroslav's Varangian force gets crushed by Mstislav's Severian levies and southern (Circassian, Alan, Pecheneg) knightly retinue. The shift towards cavalry changes the cost of maintaining private armies, leads to the rise of a sort-of-feudalism, and makes little distinction between Khazars, Hungarans, Slavs, Pechenegs, Cumans, Black Hat, Finnic, Nordic, Polish, Armenian...whatever....in princely service. Family ties back in Norway are no advantage at all by mid-1100s.
The only use of Varangians is that they are allowed to be money-changers along with the Jews and likewise get targetted in city mob riots. Militarily they are nothing special and have basically been involved in a long string of defeats. Demographically they can't compete with the Slavs (Russia reached the Pacific by the time Sweden got serious about Lappland). Culturally and materially the Baltic advantage (also probably enjoyed by archeologically/onomastically-attested Prussian and Wendish settlers of early Novgorod) disappears by the mid-10th c.
Kiev's clerics look to Constantinople, Denmark and Norway's to Bremen. There's no shared culture any more.
By the early 1100s, Russia has delineated tax districts from the White Sea to the Dniepr Rapids, a single nominal exchange currency, and tell-tale mass-produced goods which identify the settlement as "definitely Rus" from the Donets to Ladoga (writing styluses and stone spinning weights from Ovruch). None of that needs any Scandinavians at all.
It's a hard general trend to buck.