I believe that it is highly likely that focusing the question on the competence of the business analyst is looking for problems in people rather than in the surrounding system.
Although I would expect a business analyst to have expertise in requirements engineering - eliciting requirements from stakeholders, analyzing requirements for conflicts, working with the technical team to convert the user and business requirements into a format that can be used to design and build a solution, and dealing with changes to the requirements - it takes time to develop context and domain-specific knowledge to apply this knowledge to a new environment.
I would not expect that the newly hired BA would be able to fully function in two weeks. In my experience, onboarding a new employee may easily take 3 months. Some aspects of onboarding may go faster if they have worked in other parts of the company or have relevant industry experience, but the parts about developing a good working relationship with the team will always take time.
The most concerning behavior that I see is committing to features without working with the development team. Without seeing the context in which these commitments were made, though, I only have questions. Who was asking for the commitments? How much pressure was placed on the newly hired BA to make them? It wasn't good that they were made, but it's also possible the BA wasn't in a position to properly push back on making them.
I would expect that a BA, especially a new hire to the team, would need a lot of meetings with the developers to understand their perspective and ramp up. Perhaps there are ways to incorporate this into their onboarding training or other meetings that the team has, but the BA may not have been fully aware of the team practices in two weeks.
The ability to write good, clear requirements in a way that works for the team also takes time to develop.
Before you jump to eliminating the BA from the team, I'd recommend developing a plan to properly onboard the BA. However, if the person doesn't have the baseline business analysis and requirements engineering knowledge required to carry out the responsibilities of the position, then maybe it's best to move on. In that case, though, I'd also recommend looking at your interviewing process to understand how someone could be hired without demonstrating the baseline knowledge required for the job and find ways to resolve that issue.