The Laissez-faire management style is characterized by a hands-off approach where leaders provide teams with resources and advice, if needed, but otherwise don't interfere. This style is most effective with experienced, highly competent, and self-directed teams who are capable of performing their tasks without much supervision. In the context of the question, the project manager trusts the team and their work, indicating that they are likely using a Laissez-faire approach. References:
https://www.g2.com/articles/project-management-approach

This approach aligns with the PMBOK Guide's emphasis on collaboration and stakeholder engagement. It encourages open communication and teamwork, which are essential in a hierarchical organization where team members are not accustomed to autonomy. By involving the team in the decision-making process, the project manager can ensure that the changes are understood and accepted, thus minimizing the perception of poor performance.
: = PMBOK Guide and the PMP Examination Content Outline1, which emphasize the importance of stakeholder engagement and effective communication in project management. Additionally, the Professional in Business Analysis Reference Materials support the need for collaboration and communication in managing changes and aligning with organizational objectives2.

In a stressful situation, it is crucial for the project manager to establish a productive environment where team members can support each other. This approach aligns with the principles of team management in the PMBOK, which emphasizes the importance of a collaborative project team environment that facilitates individual and team learning and development, as well as optimal contributions to deliver desired outcomes1. Additionally, the PMI's tips on managing stress suggest fostering an environment where team members can rotate duties and assist each other, which can help sustain productivity and reduce stress2.
References:
PMBOK Guide - Seventh Edition3
Pro Tips: How to Manage Stress - Project Management Institute2
12 Principles of Project Management1

According to the PMBOK Guide, when a team member fails to meet a commitment, the project manager should first seek to understand the reasons for the failure. This involves meeting with the team member to discuss the situation. The goal of this meeting is not to reprimand the team member, but to develop a plan to avoid similar situations in the future. This could involve additional training, adjusting the workload, or improving communication. The other options (A, B, C) might be appropriate in some situations, but they do not address the root cause of the problem and do not provide a proactive solution to prevent similar issues in the future. References: Project Management Body of Knowledge (PMBOK) Guide, 6th Edition, Section
9.5.2.1: Develop Team: Tools and Techniques.