In a planning workshop the team breaks down the product backlog increment and can assign work to members of the team. This is referred to as:

The activity described is task planning, which is a core part of iteration planning in agile methodologies. During this event, the delivery team selects a set of product backlog items for the upcoming increment. They then decompose these items (such as user stories) into smaller, more granular tasks required to complete the work. Team members then typically self-assign or are assigned these tasks. This process focuses on how the team will accomplish the selected work within the iteration.

A. Release planning: This is a higher-level planning activity that determines the features and timeline for a product release, which typically spans multiple iterations.
C. Resource planning: This is a broader, often traditional, project management term for allocating all types of resources (people, budget, equipment) over a longer term.
D. User story writing: This is the act of creating and refining product backlog items, which occurs before the planning workshop described in the question.

1. IIBA, Agile Extension to the BABOK® Guide, Version 2, 2017. Section 4.5, "Plan the Iteration," describes this process. Specifically, section 4.5.3.1, "Break Down the Work," states: "The delivery team breaks down the items into the tasks required to complete the work. This provides a more accurate basis for estimation and progress tracking." (Page 48). This directly aligns with the question's description.

2. Sutherland, J., & Schwaber, K. (2020). The Scrum Guide. The official guide to Scrum describes the Sprint Planning event. It states, "For each selected Product Backlog item, the Developers plan the work necessary to create an Increment that meets the Definition of Done... The Product Backlog items selected for the Sprint plus the plan for delivering them is called the Sprint Backlog." This planning of the necessary work is synonymous with task planning. (Page 9).