GH-42104: [C++] Fix an OTel test failure and remove needless logs

[benibus]

Rationale for this change

Follow-up to #39905, as some issues popped after merging.

What changes are included in this PR?

• Fixes tests failing due to the ARROW_LOGGING_BACKEND env var not being defined
• Removes example log statements accidentally left in PR

Are these changes tested?

Yes

Are there any user-facing changes?

No

• GitHub Issue: [C++][CI] ARM64 Ubuntu Flacky test TestLogging.Basics in arrow-telemetry-test #42104

[lidavidm]

Approved assuming CI passes (though I see some failures; since it's MATLAB etc maybe those are flakes?)

[benibus]

though I see some failures; since it's MATLAB etc maybe those are flakes?

Took a closer look and the failures seem unrelated to me.

[kou]

The MATLAB failure is #42015 and it'll be fixed by rebasing on main.

[pitrou]

@github-actions crossbow submit -g cpp

[pitrou]

If these tests need an env var to be set, can it be set 1) either in the test setup (if not too late) 2) or in ci/scripts/cpp_test.sh? It would be better than skipping this test on many different CI configurations.

(it would probably be better if the tests could be made independent of the environment, btw, but I realize that may be difficult depending on implementation specifics)

[github-actions]

Revision: 3870d7b

Submitted crossbow builds: ursacomputing/crossbow @ actions-ee903ae6eb

Task	Status
test-alpine-linux-cpp
test-build-cpp-fuzz
test-conda-cpp
test-conda-cpp-valgrind
test-cuda-cpp
test-debian-12-cpp-amd64
test-debian-12-cpp-i386
test-fedora-39-cpp
test-ubuntu-20.04-cpp
test-ubuntu-20.04-cpp-bundled
test-ubuntu-20.04-cpp-minimal-with-formats
test-ubuntu-20.04-cpp-thread-sanitizer
test-ubuntu-22.04-cpp
test-ubuntu-22.04-cpp-20
test-ubuntu-22.04-cpp-emscripten
test-ubuntu-22.04-cpp-no-threading
test-ubuntu-24.04-cpp
test-ubuntu-24.04-cpp-gcc-14

[kou]

@pitrou Can we merge this? I want to fix CI failures on main.

[conbench-apache-arrow]

After merging your PR, Conbench analyzed the 7 benchmarking runs that have been run so far on merge-commit 59267e0.

There were no benchmark performance regressions. 🎉

The full Conbench report has more details. It also includes information about 6 possible false positives for unstable benchmarks that are known to sometimes produce them.