Write a method that sorts a list of strings alphabetically in ascending order. The method should handle case-insensitive sorting and return a new sorted list without modifying the original.

Handle null input by returning null and empty lists by returning an empty list.

Examples:

List<String> sorted = sortStringsAlphabetically(new List<String>{'banana', 'Apple', 'cherry'});
// Returns: ['Apple', 'banana', 'cherry']

List<String> empty = sortStringsAlphabetically(new List<String>());
// Returns: []

List<String> nullInput = sortStringsAlphabetically(null);
// Returns: null
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