Merge overlapping and adjacent ranges

Given an unsorted list of integer ranges represented as half-open intervals [start, end) with start < end, merge all overlapping or directly adjacent ranges and return the merged list sorted by start. Also return the total length covered by the merged ranges. For example, merging [1, 4), [3, 5), and [5, 7) yields [1, 7) and total length 6. Implement an efficient solution and analyze time and space complexity. Consider edge cases such as single-point gaps, negative values, very large inputs, and stability of the original ordering when ranges are identical.