The correct way to put an organization on the proper path to changing their mindset to an agile approach involves a shift in the way the company views, reviews, and assesses employees. This is because an agile mindset is about being flexible and adaptable. It's about individuals or even entire companies having an agile understanding of values and, as a result, acting in an agile manner1. It's not just about hiring employees who specialize in agile approaches or assigning employees to agile projects. It's about changing the culture of the organization, which includes how employees are viewed, reviewed, and assessed2. References: Mooncamp, Forbes

According to the PMBOK Guide, the project manager should assess the situation to understand how the organization's culture impacts the decision-making process, and coach the team toward a new model. This is because the project manager is responsible for facilitating the team's decision-making process and ensuring that it aligns with the agile principles and values1. The project manager should also consider the following factors that may affect the team's decision-making process2:
The level of empowerment and autonomy given to the team by the organization and the stakeholders The degree of collaboration and communication among the team members and with other parties The availability and quality of information and data to support the decision-making process The complexity and uncertainty of the project environment and the product requirements The time and resource constraints and the impact of delays on the project outcomes The potential risks and opportunities associated with the decisions and the alternatives The feedback and learning mechanisms to evaluate and improve the decision-making process The project manager should coach the team toward a new model of decision-making that is more agile and adaptive, such as the following3:
Decentralized decision-making: The team members are empowered to make decisions within their scope of work and authority, without waiting for approval from higher levels of management. This can increase the team's speed, efficiency, and ownership of the decisions.
Collaborative decision-making: The team members work together to make decisions that benefit the project and the stakeholders, rather than competing or conflicting with each other. This can enhance the team's creativity, innovation, and quality of the decisions.
Data-driven decision-making: The team members use empirical evidence and data to support their decisions, rather than relying on assumptions or opinions. This can improve the team's accuracy, reliability, and transparency of the decisions.
Iterative decision-making: The team members make decisions in small increments and cycles, rather than in large batches and phases. This can allow the team to adapt to changing conditions and feedback, and to deliver value early and frequently.
Value-based decision-making: The team members make decisions that maximize the value delivered to the customer and the stakeholders, rather than focusing on the cost or the schedule. This can ensure the team's alignment with the project vision and goals.
References:
PMBOK Guide, 6th edition, section 9.4.2.3
PMBOK Guide, 6th edition, section 9.4.2.4
Decision-Making Models: Five Agile Methods to Help You

In a project, when a task on the critical path is at risk of delaying the schedule, it's crucial for the project manager to identify any impediments that might be causing the delay. In Agile methodologies, such as Scrum, this is often done during daily standup meetings. If a team member has been providing the same update for several days, it may indicate that they are facing a blocker. The project manager should ask the team member if there is an impediment and help to remove the blockers. This approach promotes problem-solving and helps keep the project on track. References: PMBOK Guide, 6th Edition, Section 8.3 - Control Schedule

Delegating decision-making authority to team members can help alleviate delays caused by the project manager's unavailability due to meetings or other commitments. This approach empowers team members to make decisions on certain tasks without waiting for the project manager, thus maintaining project momentum and efficiency. Effective delegation involves assigning the right tasks to the right people and providing them with the necessary authority and responsibility to complete those tasks12.
References:
"Delegation and sharing of authority by the project manager" from the Project Management Institute1.
PMBOK Guide's discussion on group decision-making processes and the importance of delegation within project teams2.