Do you capture one-on-one conversations when evaluating Agile maturity, or just team data?

A mature agile team will inspect and adapt as closely as possible to the time and place of work being carried out. Team members will be careful not to put situational awareness in delay.

In theory, individual contributions aren't something that would matter in evaluating a team's ability to be agile.  The team's ability to consistently deliver work that the stakeholders want to use at a time that they need to use is it is the important thing.  And since an agile team will constantly be evaluating their own ability to do that, there really isn't anything worth tracking. 

However, since you used Agile and not agile you are asking something completely different. Let me explain why. The manifesto for agile software development provided 4 values and 12 principles that are important for teams that want to be able to adapt quickly to change. That is a team that wishes to be agile. The word agile is loosely defined as able to move quickly and easily. Animals like the leopard and deer are agile.  The word Agile was created by people that wanted to capitalize by creating processes, methodologies, and rules after the manifesto was published . What you are asking about is related to those processes, methodologies, and rules. 

So, to answer your question, you should capture anything that you can claim to be relevant to what ever variation of Agile you are trying to establish and support. But it doesn't mean that you are actually helping teams to be more agile in their actions and value production. It means you are gathering metrics to help you justify your job. 

The real thing that matters is that team(s) of individuals work together consistently delivering usable increments of work that the stakeholders find valuable.  And that it is done in a way that the teams can efficiently gather feedback from the stakeholders and quickly adapt their future work taking that feedback into account. 

I'll add one more thing to this since you posted this in a scrum.org forum.  The Scrum framework, as defined in the Scrum Guide (https://scrumguides.org/scrum-guide.html), does not say anything about metrics or measurements. Scrum existed before the manifesto was created and both of the authors of the Scrum Guide were present at summit that created the manifesto. It is one of the most popular frameworks for software development but it is not the only way that a team can be agile.  It is a framework that provides some guidance and boundaries within which you can build processes that enable success.  

What is the Scope of the Agile maturity evaluation? Team level or Organization level. 

The team's ability to deliver value is critical and not just individual contributions. As @Daniel pointed out use the 4 values and 12 principles while doing your evaluation. One on one conversations can be done with Agile coaches of the teams and try to get their inputs/frustrations. Team metrics/data like average velocity might be misleading and could lead to the organizations comparing teams based on velocity. Instead focus on value delivery (what is the definition of value? how do we measure it ?). Team dynamics and agile mindset and culture are also critical.

At an organization level you might have to also gauge the support from the upper management to enable self-managing teams and decentralizing decision making to where the work is being done. Many organizations might be doing Scrum and claim to be agile but essentially, they continue with waterfall and their value delivery is much slower. These things need to be pointed out and there should be a need created for change.