Replicator not respecting `localizable: false`

[martyf]

Bug description

On a multi-site, an Entry blueprint has a Replicator, with localizable: false.

On the origin, it is editable - correct.

On a page for the other languages, the child fields are still editable - incorrect.

I cannot add new Sets to the other language Replicator, but I can edit the fields within each Replicator. They do not correctly save.

This is also an issue if you have a Grid/Replicator within a Set for a Replicator.

Untitled.mov

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How to reproduce

1. New Statamic 6 site, with Pro enabled
2. Run php please multisite
3. Add a second site
4. Edit the Pages collection to be for both Sites
5. Edit the Blueprint, and add a Replicator. Within a set, add a single Text field. Ensure localizable: false

Logs

Environment

Environment
Application Name: Statamic
Laravel Version: 13.2.0
PHP Version: 8.4.19
Composer Version: 2.9.5
Environment: local
Debug Mode: ENABLED
URL: localise.test
Maintenance Mode: OFF
Timezone: UTC
Locale: en

Cache
Config: NOT CACHED
Events: NOT CACHED
Routes: NOT CACHED
Views: CACHED

Drivers
Broadcasting: log
Cache: file
Database: sqlite
Logs: stack / single
Mail: log
Queue: sync
Session: file

Storage
public/storage: NOT LINKED

Statamic
Addons: 0
Sites: 2 (Statamic, Other)
Stache Watcher: Enabled (auto)
Static Caching: Disabled
Version: 6.7.2 PRO

Installation

Fresh statamic/statamic site via CLI

Additional details

No response