Quick reply...
Stock clock-ui stores its list of world clocks in /home/user/.clock/wdb-user. If you have n world clocks, size of the file is 4*n, as displayed by "ls -lah /home/user/.clock/wdb-user". However, I don't know exactly how it converts an added world clock into the information stored within this file. It does not seem to be human-readable.
Best wishes.
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Per aspera ad astra...