You're quibbling. The portion covered by the congestion charges is a tiny, tiny portion of the whole of London, comprising mostly business and entertainment areas.
The point I am making is that Americans use the naming confusion to draw the fundamentally misleading comparison.
Only if you don't know anything about Manhattan other than "density".
The now-canceled project would have affected, at a minimum, about 10% of New York's entire resident population (~800k). A lot of New Yorkers actually live in Manhattan south of 60th. That's part of why it's dense.
A more reasonable comparison to the current London congestion area would be midtown -- the small area in the middle of Manhattan with the obvious skyscrapers, as well as Times Square, theaters, throngs of tourists, and the bulk of finance.
You can't compare land areas directly. London is twice the size of New York. Population density, land uses, etc. are completely different.
For example, only about 140k people [1] live in the London area. Easily 800k live in the Manhattan area, and probably more (population density is higher on the lower half of the island, due to things like Central Park).
https://tfl.gov.uk/modes/driving/congestion-charge/congestio...