refactor: avoid deprecated nvim_out_write/nvim_err_write #322

Job	Run time
lint	28s
test-upstream (python 3.12, windows-latest)	3m 33s
test-upstream (python 3.12, ubuntu-latest)	1m 4s
test-upstream (python 3.12, macos-latest)	1m 11s
test (python 3.14, nightly, windows-latest)	1m 20s
test (python 3.12, stable, windows-latest)	1m 8s
test (python 3.12, stable, ubuntu-latest)	28s
test (python 3.13, nightly, windows-latest)	1m 31s
test (python 3.12, nightly, ubuntu-latest)	26s
test (python 3.10, nightly, macos-latest)	1m 8s
test (python 3.14, nightly, macos-latest)	53s
test (python 3.11, nightly, ubuntu-latest)	29s
test (python 3.14, nightly, ubuntu-latest)	30s
test (python 3.12, nightly, macos-latest)	55s
test (python 3.11, nightly, windows-latest)	1m 9s
test (python 3.13, nightly, ubuntu-latest)	29s
test (python 3.10, nightly, windows-latest)	1m 19s
test (python 3.11, nightly, macos-latest)	59s
test (python 3.13, nightly, macos-latest)	46s
test (python 3.12, nightly, windows-latest)	1m 16s
test (python 3.10, nightly, ubuntu-latest)	34s
test (python 3.12, stable, macos-latest)	59s
	22m 35s

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