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Please don’t ask how I stumbled upon this but please try the following:
However, February 29th, 1900 never occurred since 1900 was not a leap year (see Wikipedia).
Is this a bug or am I missing something?
No, it is not a bug in Excel and yes you are missing something.
Excel implemented the dates to match with Lotus 1-2-3 for which compatibility was required at the time so was designed to have this error. Lotus 1-2-3 had the bug of thinking 1900 was a leap year.
See Microsoft’s documentation for the reasons why not to fix it.