tee: remove ErrorKind::Other, simplify already discarded Result

[oech3]

This should avoid confusion caused by strange usage of ErrorKind::Other.
Closes #12952 .

[codspeed-hq]

Merging this PR will not alter performance

✅ 323 untouched benchmarks
⏩ 46 skipped benchmarks¹

---

_{Comparing oech3:tee-1 (dd23e86) with main (8464759)}

Footnotes

1. 46 benchmarks were skipped, so the baseline results were used instead. If they were deleted from the codebase, click here and archive them to remove them from the performance reports. ↩

[github-actions]

GNU testsuite comparison:

Skip an intermittent issue tests/tail/retry (fails in this run but passes in the 'main' branch)
Skipping an intermittent issue tests/tail/tail-n0f (passes in this run but fails in the 'main' branch)