Look at the technology and the product road map. If there isn't one, help creating one
Actively look around for new technologies, new parts or new vendors that are relevant to your business and/or products
Get a bunch of eval board, bring them up and do some performance measurements or some cool demo of what may be possible with the stuff
Question: What should I do?
Question here is: Is there no technical / hands-on work for the company / department as a whole, or there are assignments but you're not assigned one?
Either way, given your situation that you already tried the below:
Informing your superiors about the problem you're facing with the nature of work assigned to you
Build two lists
List 1: things you want to do
List 2: things that you think will add value to your group
Walk to your manager and say,
“I’ve got some bandwidth and I want to check with you if you have something for me, if not, I can do any of these...”
Items that appear on both list 1 and list 2
Items that appear on list 1
Items that appear on list 2