The elicitation technique that the business analyst should use to gather information about the steps a user takes to accomplish a goal, challenges a user faces, people the user interacts with, applications they use to complete the steps, and their level of morale as they move through the process is journey mapping. Journey mapping is a technique that creates a visual representation of a user's experience with a product or service over time. It can help the business analyst understand how a user interacts with a product or service across different touchpoints or stages, what pain points or obstacles they encounter, what emotions or feelings they have, etc.
Survey/Questionnaire is an elicitation technique that collects quantitative or qualitative data from a large number of stakeholders using predefined questions or scales. It can help the business analyst measure stakeholder satisfaction, preferences, or feedback, but not capture the details or nuances of their experience.

Explanation
This answer suggests shadowing as the next step for the BA to uncover the issue and propose a business solution for CK's distribution challenge. Shadowing is a technique where the BA observes how a user performs their tasks in their natural environment. Shadowing helps to gain insights into the user's workflow, challenges, pain points, and opportunities for improvement.
References:https://trailhead.salesforce.com/en/content/learn/modules/salesforce-business-analyst-quick-look/use

The business analyst should prioritize US-4007 and US-4009 because they are the most critical work items.
US-4007 is the work item that will allow customers to submit support tickets, and US-4009 is the work item that will allow customer service representatives to view and respond to support tickets. These two work items are essential for the MVP to be functional.
US-4008 is a less critical work item because it will allow customers to track the status of their support tickets.
This work item is important, but it is not essential for the MVP to be functional.
US-4010 is the least critical work item because it will allow customers to rate the quality of customer service.
This work item is important, but it is not essential for the MVP to be functional.
In conclusion, the business analyst should prioritize US-4007 and US-4009 because they are the most critical work items. These two work items are essential for the MVP to be functional.

The elicitation technique that the business analyst should use to gather information about the steps a user takes to accomplish a goal, challenges a user faces, people the user interacts with, applications they use to complete the steps, and their level of morale as they move through the process is journey mapping. Journey mapping is a technique that creates a visual representation of a user's experience with a product or service over time. It can help the business analyst understand how a user interacts with a product or service across different touchpoints or stages, what pain points or obstacles they encounter, what emotions or feelings they have, etc. Survey/Questionnaire is an elicitation technique that collects quantitative or qualitative data from a large number of stakeholders using predefined questions or scales. It can help the business analyst measure stakeholder satisfaction, preferences, or feedback, but not capture the details or nuances of their experience.