Final cleanup after all secret categories have been migrated to AWS Secrets Manager.

Prerequisites

• RUBY-3672 (AWS auth secrets) — done
• FLE/CSFLE secrets migration ticket — done
• Kerberos secrets migration ticket — done
• Atlas connectivity secrets migration ticket — done
• RUBY-3725 (test runner consolidation) — done

Scope

1. Remove the "delete private environment" function from common.yml.erb and all task references to it
2. Remove all .env.private fallback paths from shell scripts (run-tests-aws-auth.sh, functions-aws.sh, functions-kerberos.sh, and any others)
3. Remove the "export FLE credentials" and "export Kerberos credentials" function stubs if not already deleted in prior tickets
4. Verify no .env.private writes remain anywhere under .evergreen/
5. Coordinate with Evergreen project admins to delete the migrated project variables from Evergreen project settings (all 49 variables identified in RUBY-3311 analysis)
6. Confirm aws_key / aws_secret (S3 artifact upload) disposition with DevProd — infrastructure vars, may stay or be handled separately

Files to change

• .evergreen/config/common.yml.erb and regenerated .evergreen/config.yml
• Any remaining .evergreen/*.sh files with .env.private references

Test plan

Full CI patch run to confirm no regressions. Verify no tasks fail due to missing .env.private.