Do I need to report carpal tunnel syndrome as a long-term health condition, or does it go away after being treated?

Report it. Theyll know anyway. Surgery cures it most cases.
CTS. Some cases of cts can be treated conservatively with splinting and steroid injections, but most cases are treated surgically with a carpal tunnel release with relatively few recurrences. In most cases, cts doesn't lead to long term disability.
Yes. Carpel tunnel some could resolve with no sequence, some time it cold go on for long time even when treated especially if the continue doing the same job. Good luck thank you.