Split out integration test plumbing (#2594) (#2300)

[tustvold]

Which issue does this PR close?

Part of #2594
Part of #2300

Rationale for this change

The way the integration test plumbing is muddled with the core logic is incredibly confusing, and complicates splitting apart the crates (#2594) and adding features flags (#2300)

What changes are included in this PR?

This moves the integration test plumbing to the existing integration-testing. I originally moved it to a separate crate, but this seemed redundant

Are there any user-facing changes?

Technically this functionality was being published, it now isn't. I have confirmed DataFusion isn't making use of this.

[tustvold]

This is a drive-by cleanup

[ursabot]

Benchmark runs are scheduled for baseline = 6ab208c and contender = c6e7680. c6e7680 is a master commit associated with this PR. Results will be available as each benchmark for each run completes.
Conbench compare runs links:
[Skipped ⚠️ Benchmarking of arrow-rs-commits is not supported on ec2-t3-xlarge-us-east-2] ec2-t3-xlarge-us-east-2
[Skipped ⚠️ Benchmarking of arrow-rs-commits is not supported on test-mac-arm] test-mac-arm
[Skipped ⚠️ Benchmarking of arrow-rs-commits is not supported on ursa-i9-9960x] ursa-i9-9960x
[Skipped ⚠️ Benchmarking of arrow-rs-commits is not supported on ursa-thinkcentre-m75q] ursa-thinkcentre-m75q
Buildkite builds:
Supported benchmarks:
ec2-t3-xlarge-us-east-2: Supported benchmark langs: Python, R. Runs only benchmarks with cloud = True
test-mac-arm: Supported benchmark langs: C++, Python, R
ursa-i9-9960x: Supported benchmark langs: Python, R, JavaScript
ursa-thinkcentre-m75q: Supported benchmark langs: C++, Java