Try to log publish errors

[hsubox76]

Try to ensure any errors in the spawn process that runs the npm publish command are sent to the console and not swallowed. May help debug problem publishing in staging:

https://github.com/firebase/firebase-js-sdk/actions/runs/4953536908/jobs/8861115245

[changeset-bot]

⚠️ No Changeset found

Latest commit: 447f9a4

Merging this PR will not cause a version bump for any packages. If these changes should not result in a new version, you're good to go. If these changes should result in a version bump, you need to add a changeset.

This PR includes no changesets

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[dwyfrequency]

LGTM

[google-oss-bot]

Size Report ¹

Affected Products

No changes between base commit (6d332b4) and merge commit (753ab65).

Test Logs

• Base (6d332b4): https://github.com/firebase/firebase-js-sdk/actions/runs/4953191623
• Merge (753ab65): https://github.com/firebase/firebase-js-sdk/actions/runs/4960805165

1. https://storage.googleapis.com/firebase-sdk-metric-reports/rXFErvmgJ0.html

[google-oss-bot]

Size Analysis Report ¹

Affected Products

No changes between base commit (6d332b4) and merge commit (753ab65).

Test Logs

• Base (6d332b4): https://github.com/firebase/firebase-js-sdk/actions/runs/4953191623
• Merge (753ab65): https://github.com/firebase/firebase-js-sdk/actions/runs/4960805165

1. https://storage.googleapis.com/firebase-sdk-metric-reports/jIVqRxwhca.html