[codex] Fix builder code parsing in register script

[Kubudak90]

Summary

• parse the builder code API response with jq instead of a whitespace-sensitive grep pattern
• add a shell regression test that fakes the API response with pretty-printed JSON

Root cause

The register script searched for "builder_code":"...", so valid JSON with a space after the colon produced no match. Because the script runs with set -euo pipefail, the failed grep could exit before the existing empty-value guard ran.

Fixes #54.

Validation

• bash -n skills/build-on-base/scripts/register.sh
• bash -n skills/build-on-base/scripts/register_test.sh
• bash skills/build-on-base/scripts/register_test.sh

[cb-heimdall]

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