How would you handle a requirement that a user can save a long application partway through and resume it days later?

Salesforce provides this natively, and the interesting part of the answer is what you have to think about beyond flipping the setting.

1. Enable Save For Later on the OmniScript so the in-progress data JSON is persisted and the user can resume at the point they left.
2. Decide what resumes: the data JSON is restored, but anything fetched from an external system at the start may now be stale. Reference data that could have changed should be re-fetched on resume rather than trusted from the saved state.
3. Think about who can resume. If the application can be picked up by a different user — an agent continuing a customer's self-service application — the resume path and the record's sharing need to support that.
4. Consider expiry and cleanup. Half-finished applications accumulate; agree with the business how long they should live and how they are removed or reported on.
5. And handle version drift: if the OmniScript is updated between save and resume, be clear about whether in-flight applications continue on the old version or are restarted. This is a business decision, not just a technical one.