Four strange places to see London's Roman Wall

https://en.wikipedia.org/wiki/City_of_London

Title should probably read "the City of London" rather than "London".

Here is the US, the "city of Chicago" is the same as "Chicago".

The UK does not require this layer of subdivision to exist, so it's not that there's a different county or set of counties covering the same area now but rather there is no county. This is a contrast to say the US system where AIUI there must be a county and in some cases that county doesn't really matter (e.g. New York County in New York City aka Manhattan) but it has to exist anyway.

City status is very different here, the Monarch (ie now Charlie) gets to decide what is or is not a city, but because that's arbitrary it also has very few consequences, it's a cosmetic basically, you can write "City" on some signs if you like, but if you feel like a small town you still feel like a small town, and if you already feel like a bustling city then having the word doesn't make a real difference.

There are other offenders, but the US and UK together are probably the main reason English no longer has concise but unambiguous way to refer to sovereign states

The latter part is true of exactly one US state (Hawaii), but otherwise false. They are called that because they are political bodies capable of international relations. The 13 founding states were British colonies; Florida, New Mexico and Texas were famously Mexican and/or Spanish colonies, and the western half of the continental states were French colonies (though largely unexplored by France, so only nominally held).