GH-48766: [CI][Packaging] Delete conan related packaging jobs and CI

[raulcd]

Rationale for this change

The conan CI jobs have been failing for 4+ months. The main problem is that conan deprecated the repository they used to build the Docker files we were using:

⛔ This repository is now deprecated. The Docker recipes and images provided by this repository are no longer used by ConanCenterIndex CI. Users are encouraged to explore alternative solutions for their Docker image needs.

see:
https://github.com/conan-io/conan-docker-tools#readme

What changes are included in this PR?

Remove all conan related Arrow CI. The integration will have to be managed upstream when we build the PRs to conan. This might required patches and take longer but having the CI jobs broken for 4+ months without a clear guideline on how to proceed should be fixed.

Are these changes tested?

No

Are there any user-facing changes?

No

• GitHub Issue: [CI][Packaging] conan-minimum and conan-maximum jobs are failing #48766

[raulcd]

@kou should we do this?

[github-actions]

⚠️ GitHub issue #48766 has been automatically assigned in GitHub to PR creator.

[kou]

+1

Yes!

[conbench-apache-arrow]

After merging your PR, Conbench analyzed the 3 benchmarking runs that have been run so far on merge-commit 99ca031.

There was 1 benchmark result with an error:

• Commit Run on amd64-m5-4xlarge-linux at 2026-04-02 17:02:55Z
  • file-write (Python) with compression=snappy, dataset=nyctaxi_2010-01, file_type=parquet, input_type=dataframe

There were no benchmark performance regressions. 🎉

The full Conbench report has more details. It also includes information about 114 possible false positives for unstable benchmarks that are known to sometimes produce them.