Is digital transformation about moving existing processes onto computers, or does it require completely redesigning them?

Both can be correct, but the sequence matters. Simply moving old processes to a new system usually just digitalizes existing problems without solving the underlying efficiency issues. A more practical approach is: first walk through your current processes and identify which steps are done that way because of 'paper or email limitations,' and which are true business logic. For the former, you can adjust while digitalizing; for the latter, the system should adapt to your rules, not the other way around. This clarification process itself requires cross-department communication, and often exposes the fact that different teams have been operating with different understandings. This is not a bad thing—it's an opportunity to surface hidden problems.