Cleanup ApplicationDefaultCredentials

[tustvold]

Which issue does this PR close?

Relates to #3797

Rationale for this change

It was unclear how to extend the existing logic to support the different authentication flows, and the error messages were not always particularly clear on what the actual issue is.

What changes are included in this PR?

Are there any user-facing changes?

[alamb]

cc @wjones127 @Samrose-Ahmed @winding-lines

[winding-lines]

Looks good to me, thanks for the cleanup!

[ursabot]

Benchmark runs are scheduled for baseline = 79518cf and contender = 7eb588d. 7eb588d 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