Ask the team.
With good implemented Agile the team decides how to do the work, not just you, nor a manager. I would expect any team member that can program to be involved in most of not all major design decisions. So yes I would expect the QA engineer to help with the design and architecture and not just the automation frameworks.
Extreme programming has some usefull terms like TUBE to measure simplicty, the code should be Testable, Understandable, Browsable and Explainable. A senior QA can try to motivate the team to use practises like this to make better quality code.
Personally I am also a teacher of Clean Code practises, which are necessary to make the product Agile, not just the process. Read more about technical excellence it contains a lot of testing stuff. This is often overlooked in Agile teams who are doing mostly cargo cult Scrum.
In the end people should be doing stuff they are comfortable with and that adds the most value to the team. So again ask the team what they expect from the QA engineer and the QA engineer can explain what he/she has to offer with their experience.
Keep in mind that you should not focus to much in disciplines as a QA role. Agile teams should consists of T-shaped people who have broad software development skills with one or two specialisation that they teach to others. This to minimize the teams bus factor.