GH-48102: [Python] Remove deprecated Array.format method

[EslamAhmed171]

Rationale for this change

This PR removes the deprecated Array.format method as requested in issue #48102.

What changes are included in this PR?

• Removed the deprecated Array.format method from the Python API
• The method will be automatically removed from the documentation (https://arrow.apache.org/docs/python/generated/pyarrow.Array.html) as it's auto-generated from the source code

Are these changes tested?

Yes, existing tests continue to pass.

Are there any user-facing changes?

This PR includes breaking changes to public APIs.

The deprecated Array.format method has been removed. Users who have not migrated from this deprecated method should use Array.to_string() instead. This change was announced in the deprecation warning since 2020.

Migration:

# Old (deprecated)
array.format()

# New
array.to_string()
* GitHub Issue: #48102

[github-actions]

⚠️ GitHub issue #48102 has been automatically assigned in GitHub to PR creator.

[github-actions]

⚠️ GitHub issue #48102 has been automatically assigned in GitHub to PR creator.