I found a quote giving a hint about how quickly the Fog moves. "An Archbishop is too important for the house to take any risks. If anything happens to me - the Fog will absorb House Serpis in mere weeks." They do their rituals daily to keep the Fog away, but it would take weeks to absorb their territory if they stop. Also notice there is no mention of other Houses being affected first -- which supports my interpretation of radial slices for each House (adjacent territories bounded on one edge by the city wall) instead of concentric rings.
How much distance does the Fog need to cover in weeks to fully absorb House Serpis?
If the longest distance between any two points in the city is 3 miles (based on average human walking speed and the observation that anywhere in the city is reachable with 1 energy), then the Fog needs to travel at most 3 miles (plus the distance from where the Fog edge is now to the city wall). Suppose the distance from the city walls to the Fog is the same as the radial dimension of White Town, meaning that the distance the Fog must travel to absorb House Serpis fully is equal to the distance from the city wall all the way through House Serpis to the city wall on the opposite side (passing through White Town). For a first approximation, it will do.
So, the Fog will travel 3 miles in mere weeks. How many weeks is "mere" weeks? It could be as few as two, and it could be any quantity not exceeding weeks. Incidentally, shouldn't it be "decades"?
If the Fog edge moves 3 miles in two decades (20 days), then we have a rate of 0.15 miles per day. Since the priests and the Fog have reached some equilibrium (otherwise why would they need to do the rituals daily?) this suggests that each ritual is able to push the Fog back by only a similar amount (say 0.14 - 0.16 miles). That raises the question of how the Fog was originally pushed back to its current position, which would require rituals capable of pushing the Fog faster than it can roll back in, and why those stronger rituals are not being used to push it even more. If the priests' rituals are consistently pushing the Fog more than the Fog is reclaiming, then the territory would be constantly expanding. One way to interpret this: the effectiveness of the rituals is non-linear and has a larger effect when the area being warded is small. As the area has grown, their effectiveness has diminished. So now, in order to maintain their current borders, they need daily rituals, whereas when the city was half its current size, weekly rituals might have sufficed.
Coming back to the assumption about the city covering an area of only 3 miles, what does that imply about population density?
If the total population is 2 million (based on colosseum spectator capacity described as hundreds of thousands), the population density is approximately 600,000 per square mile. By this calculation, the Eternal Rome is ten times more densely populated than the densest city on Earth. Yet there are images in the game of large open spaces, not packed wall-to-wall with people. Maybe they are all packed into the Anthill in the Serpentine Quarter...?
It is likely that the Colosseum in the Eternal Rome accommodates a larger percentage of the population than the one in ancient Rome did (which was 50,000 of the 450,000 total). Slaves in the Eternal Rome outnumber citizens, and not every slave would spectate each event, which argues for the Colosseum capacity being smaller than the total population to avoid empty seats, but they might want to be able to accommodate everyone ... for special occasions.
If the capacity of the Eternal Rome's Colloseum is large enough to accommodate the entire population, and we take the smallest possible value for "hundreds of thousands" (200,000), with an area of 3 square miles, then we have 66,000 per square mile. This is comparable to the most densely populated cities on Earth (Kolkata ~61,000, Mumbai ~76,000).
By exploiting verticality (building tall, with towers and underground levels), this density of population could be accommodated while still having some open spaces as shown in the game. If they built 500 levels each 14 feet high and 3 miles in width and height, the density per square mile would drop to a far-more-manageable 132. They would not build completely uniform levels like that, but this illustrates the concept. It also suggests the population may be much larger than 200,000, and that there is a limit to how far up or down they can go.