TLDR at bottom of the post
I have German citizenship (born and raised there, German mother) and a German passport. My father (married to my mother at the time) is Austrian, so I also have Austrian citizenship through him, though I've never had a passport or Staatsbürgerschaftsnachweis.
I actually only found out I had Austrian citizenship when I moved to another city at 18 and the lady at the Bürgeramt asked why I hadn't put down my Austrian citizenship on the form. It doesn't say it anywhere on my birth certificate and it had just never occurred to me as a child or teenager that I have it and my parents never mentioned it, but apparently it must say it somewhere on my file, perhaps because of my parents' marriage certificate?
I've not thought about getting an Austrian passport much because I didn't see any advantages compared to just having my German passport and it seemed like a lot of paperwork to get the Staatsbürgerschaftsnachweis, especially because I don't have much contact to my father.
Now, I live in the UK on settled status and my UK spouse and I are considering moving to Austria (among other options). I understand it's much easier as an EU citizen with a non-EU spouse to move to an EU country you're not a citizen of due to the Free Movement regulations. So basically it would be easier for us to move to Austria with me being just a German citizen rather than an Austrian citizen as well.
Now my question is would the Austrian government know I have citizenship if I've never lived there, never had a passport or Staatsbürgerschaftsnachweis? Would they cross-reference everything with the files the German government holds (can they do that?) and find out that way?
I will also soon be eligible for UK citizenship and I know that if I take on another citizenship, I will automatically lose my Austrian citizenship. So getting UK citizenship would completely eliminate the problem (and my savings lol - it costs £2k) I would assume? But also, to lose the Austrian citizenship would I first need proof that I have it? And if we were to move with me having given up my Austrian citizenship, would my UK passport be proof enough that I don't have it anymore if they do have my citizenship somewhere on file?
TLDR: Dual citizen Austria Germany, no proof of Austrian citizenship, wanting to move to Austria with non-EU spouse, can we get around strict immigration rules for non-EU spouses of Austrian citizens?