During a Sprint, when is new work or further decomposition of work added to the...

 New work or further decomposition of work is added to the Sprint Backlog as soon as possible after it is identified because:

It reflects the current state of the Sprint. The Sprint Backlog is a plan that the Developers create and update throughout the Sprint, based on their progress, learnings, and changes. By adding new work or further decomposition of work to the Sprint Backlog promptly, the Developers can ensure that the Sprint Backlog is transparent, accurate, and up-to-date.

It enables the Developers to self-manage their work. The Developers are accountable for organizing and managing their own work, and they have the authority to change the Sprint Backlog as needed. By adding new work or further decomposition of work to the Sprint Backlog promptly, the Developers can exercise their autonomy and empowerment, and adjust their plan accordingly.

It supports the achievement of the Sprint Goal. The Sprint Goal is a single objective that provides guidance and focus for the Developers throughout the Sprint. By adding new work or further decomposition of work to the Sprint Backlog promptly, the Developers can ensure that their work is aligned with and contributes to the Sprint Goal.

References:

Scrum Guide 2020, page 6: “Developers are the people in the Scrum Team that are committed to creating any aspect of a usable Increment each Sprint.”

Scrum Guide 2020, page 6: “The Developers are accountable for … organizing and managing their work.”

Scrum Guide 2020, page 10: “The Sprint Goal is a single objective for the Sprint.”

Scrum Guide 2020, page 14: “The purpose of each Sprint is to deliver Increments of potentially releasable functionality that adhere to the Scrum Team’s current Definition of Done.”

Scrum Guide 2020, page 14: “The Sprint Backlog is composed of … all of the work needed to deliver a product Increment that meets the Definition of Done.”

Scrum Guide 2020, page 14: “The Developers can change the content of the Sprint Backlog throughout the Sprint as more is learned.”