Medieval republican city-states are more generally associated with Mediterranean Europe (especially, if not exclusively, Northern Italy) and might as an oddity for a lay person.
How did it came into being? Was it issued from a tradition of assemblies in East Slavic polities? If it's the case, how did it changed (or not) from its origins?
It was surprisingly so, far moreso than one might expect given the nature of the other successor/appanage states of old Kievan Rus. Veliki Gospodin Novgorod is a unique case in that it was and is in some takes of Kievan Rus history held to be contemporary in antiquity and power with Kiev, though in other cases it's not.
There is a tradition of assemblies in Kievan Rus during its height, though they had rather less power relative to the princes of Kiev and much, much less in the appanage states like Galicia, Vladimir, and the like than Novgorod. There are two main reasons for that, and where it came to diverge from the other Rus states of the time.
The first is that the Veche, as the Novgorodians called the assembly, could hire and fire the prince at will, essentially, making it one of the most powerful assemblies in medieval times and perhaps the most democratic Rus and successor states politics have ever gotten for a lengthy period of time. This could be as much a weakness as a strength, as it ultimately proved against Ivan III and IV, and it certainly complicated the life of Alexander Nevsky, who was famous but despised and vice-versa by the Veche.
The second is that the Veche very directly refused to allow their princes a strong self-sustained army of the kind other appanage states had, relying on levies and mercenaries to substitute instead. This was the essential element in how they gained the power to hire and fire, in a certain sense, the princes.
Novgorod, too, was oriented in a different sense to Kiev or Vladimir or Galicia or the like in that it was a Baltic trading state with an Asian hinterland, which is a lot to do with why they were attacked by say, the Teutonic Knights, because the latter resented the competition.
Novgorod is further unique in being so far north in the denser woodlands of northern Russia that the Golden Horde never even made a token effort to claim its territory, meaning it was the most free Rus state of the Golden Horde years, and correspondingly also far more powerful than the city-states of Vladimir like well, Vladimir itself, or Tver, or of course the Grand Principality of Moscow.
The reason Veliki Gospodin Novgorod met the fate it did is ultimately that the Grand Princes of Moscow built a vast army they relied upon from their own resources, and an army that they could control was far more reliable than what the Veche had at its disposal, culminating in first its annexation and then its gutting under Ivan IV in one of his most demented acts where he fully lived up to his reputation as the Terrible.
Sources:
Medieval Russia, 980-1584 by Janet Martin.
Ivan the Terrible by Robert Payne.