A lot of context is missing (e.g. API design details, security policies, risk assessments etc) so answering is difficult. But, here are some thoughts:
our technical manager disagrees this improvement is needed. In his words, "pentesters have reported this as minor. I mean, we are not even exposing stacktrace here, it is fine"
so, the people whose job is to make risk assessments have already decided on the issue. Unless it's also your job to challenge that, I'm not sure what you can do to change it
I have serious concerns about it
Understandable. Based on your description, I would have concerns too. But, that's not the point; the point is that the risk has already been accepted by the people responsible to make such decisions
Is my understanding incorrect that this 'excessive exposed data' is a medium to high security risk?
Unfortunately, this cannot be answered easily. Risk is based on facts that you don't provide in your question. More details are required on how the API works, what data does it expose and the risk assessment done by the security people, before an opinion can be expressed
Also, in general:
the API should have some sort of authentication and authorization mechanism to protect it. As such, even if this info is available, maybe there are proper security controls in place (along with logging and monitoring) that mitigate the said risk
on the exposure of configuration items, it also depends on which configuration items are exposed, whether the API allows to modify them and/or which items to modify. Maybe the configuration items exposed are non-critical (security-wise) and read-only. Of course, that's still a source of understanding the system's internals which can lead to vulnerabilities identification, but - again - this falls under the risk assessment that the security people have done
whether the URLs returned are a security issue, also depends on whether the customer details are exposed to other customers or only to the customer that the URLs refer to. But (again) this must have been considered during the risk assessment done by the security people
As you can understand, everything revolves around risk assessment and the outcome of it. If the people that are responsible for it have assessed that the issues you mention are not a problem, then you should play along.
Having said that, in the past I did not approve similar API behaviour, but it was part of my job to have an opinion.