What are the responsibilities of a Functional Manager to the project teams? This varies a lot from company to company. Therefore, you’ve got to exploit the opportunities you get to interact with the project team to improve your awareness of team members performance.

Go and see for yourself (in Kanban the principle of “Genchi Genbutsu”
applies). This includes:

• Go to Stand Ups. You probably don’t need to go every day, but you should probably be going more than once a week. You’re a chicken, so don’t get too involved. Don’t be afraid not to ask difficult questions – or if you feel it would be too disruptive, you should ask the Scrum Master.
• Go to Demos. If your guys are part of a functioning Scrum team they will be running a demo every sprint. Some QA teams adopt an unhealthy attitude that they’re there to block releasing. You need to see that your testers are part of teams that always produce potentially shippable software.
• Walk around, speak to the whole team, see how they’re getting on. Don’t do it for the explicit purpose of assessing performance but do it to increase your understanding of project the team works on and how they function. As a Senior member of the QA team, you probably have expertise to offer. You should be helping to coach the team (not just your direct reports).
• Speak to your testers on a regular basis. I’ve got a preference for informal chats, preferably over a coffee out of the office. Build a rapport with your team members and they’ll let you know the areas in which they’re having difficulties which you can follow up on.

Succeeding with Agile by Mike Cohn has a section in chapter 8 about the role of Functional Manager. Well worth a read, and the part that seems most relevant:

A functional manager is responsible for providing guidance and
coaching to members of the group. ScrumMasters and product owners also
provide guidance and coaching, but their views are limited to a single
project or product. A functional manager will have a broader
perspective, including the ability to establish cross-project
standards and set expectations for quality, maintainability,
reusability, and many of the other -ilities or nonfunctional
requirements.

Functional managers also retain responsibility for developing the
people in their groups. Securing the budget and time to send them to
conferences, challenging them with appropriate projects, and
encouraging them to join or form communities of practice are all part
of the functional manager’s role.

Personnel Responsibilities

In most organizations, functional managers will retain responsibility
for writing periodic reviews of the personnel in their departments.
Although the functional manager has hopefully always incorporated
input from each employee’s coworkers and customers into the review,
the need to do so is greater in a Scrum environment because the
employee will likely be working less closely with the functional
manager on a day-to-day basis.

In many organizations, functional managers also retain responsibility
for making hiring and firing decisions. Neither the ScrumMaster nor
the product owner has this level of authority over individuals on the
product development teams.

After the organization adopts Scrum, most functional managers find
themselves with more time available than they had before. This time is
most often used to stay in closer touch with their direct reports, to
know more about each project the group’s employees are working on (by
attending various sprint reviews and so on), and to pay more attention
to cross-project standards and future directions.

Have you considered attending the scrums but not talking or participating?

If you state that you are there as a passive participant only, then you will get the information you need.

In the cases when you need follow-up information from a particular tester, you can make a mental note of the item and go ask for more details after the scrum is over.

I have seen two approaches work:

1. Go to Scrum – I’ve seen scrums where the manager attends as a “chicken”. No talking, no criticizing, no dour face. You’re there to gather information. Once everyone is comfortable with this, you can maybe ask short clarifying questions. This may not work well if your team defers to you too much.
2. Meet independently with PM/Team Lead – Even in self-organized teams someone is the project manager or team lead. They (which one depends on the organization) then become responsible for people doing good work on a day to day basis. You exist to help them raise the skill of the team as a whole, hold them accountable, and to step in when they want/need help with problems that “the boss” needs to deal with. This may not work well if you micromanage too much, or lack a person on the team to fill that role.