Emotional intelligence (EI) is the ability to understand and manage one's own emotions, as well as the emotions of others. A project manager with high EI is more likely to be aware of and control their behavior, understand the impact of their actions on the team, and maintain positive relationships. The scenario described suggests a lack of such awareness and management, indicating a deficiency in EI rather than a lack of empathy, training, or being in the wrong role.
References: While the specific references from the Professional in Business Analysis Reference Materials are not provided in the search results, the concept of emotional intelligence and its importance in project management is widely recognized in the field. For a deeper understanding, one can refer to the PMI's foundational standards and guides, such as the PMBOKGuide and the PMI Guide to Business Analysis, which include discussions on team dynamics and the soft skills necessary for effective project management1234.

When a project manager encounters a situation where a vendor's rates do not fit into the project budget, it's important to engage the project stakeholders1. This is because stakeholders have a vested interest in the project and can provide valuable input on how to proceed. They may be able to suggest alternative vendors, provide additional funding, or help negotiate a better rate with the vendor. Engaging stakeholders in this decision also ensures transparency and buy-in, which are key to successful project management2. References:
https://www.brainscape.com/flashcards/pmp-test-11-10971072/packs/19294018
https://relevant.software/blog/it-vendor-management-guide/

The best course of action is for the project manager to facilitate a session with all stakeholders to discuss, agree upon, and document the benefits and their ownership. This aligns with the PMP objectives of engaging stakeholders in the project decision-making process, including benefit analysis and distribution. It ensures that all parties have a clear understanding and agreement on how the benefits will be shared and utilized, which is crucial for project success and stakeholder satisfaction.
= This approach is supported by the PMI's guidance on conducting benefit analysis with stakeholders to validate project alignment with organizational strategy and expected business value1. Additionally, the PMI's standards on project benefit management emphasize the importance of defining and appraising target benefits during project initiation, which includes stakeholder involvement2.