This depends on your exact definition of an FHE computation. You could imagine a definition under which you can consider the whole scheme a single Turing comple

This depends on your exact definition of an FHE computation. You could imagine a definition under which you can consider the whole scheme a single Turing complete FHE. But this definition would have to accept that the FHE computation is unbounded and leaks computation length (as would any Turing complete scheme). I don't like the name "termination oracle", it sound too much like "halting oracle" which is not what is going on here. All we do is add an outer while-loop, a simple algorithmic transformation. I wouldn't even consider that an oracle.