Localized fields show fallback values after publish

[TomSteer]

Describe the Bug

Publishing a document in a non-default locale causes localized fields to show fallback values from the default locale. A full page reload shows the correct state. Seems like the publish action in PublishButton doesn't pass 'fallback-locale': 'null' like saveDraft and document reads do.

Link to the code that reproduces this issue

https://github.com/payloadcms/payload/blob/main/packages/ui/src/elements/PublishButton/index.tsx#L165-L172

Reproduction Steps

1. Have localization enabled with a fallback locale
2. Set a localized field in the default locale
3. Switch to another locale, edit a different field, publish
4. Localized field shows the default locale's value until you do a full page reload

Which area(s) are affected?

area: core

Environment Info

payload: 3.80.0