ICU-22954 Revert to using std::u16string instead of UnicodeString

[roubert]

It seems as if icu4c-windows-cygwin-gcc only crashes if the constructor is defined inline, so with the exception of the constructor this commit reverts the code to commit 320220e.

Checklist

• Required: Issue filed: ICU-22954
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• Issue accepted (done by Technical Committee after discussion)
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