This page appears to describe the standardized process for registering to vote as an overseas absentee voter: www.fvap.gov/citizen-voter/
It states that whether or not you just want to vote for federal offices, the important criteria is to establish your “voting residency”, and then the elections office of that county would send you a ballot for what you’re eligible to vote for. Your last US address appears to be the predominant determinator, even if you have no more ties to it.
I can’t imagine this will be simple to navigate, but I applaud you for seeking to exercise your important civil right to vote. Good luck!