Incorrect taxonomy term linked to multi-site collections in REST API

[andrazperson]

Bug description

When fetching all collection entries using GET /api/collections/{collection}/entries, the taxonomy term is not correctly localized. Works normally when fetching a specific collection entry GET /api/collections/{collection}/entries/{id}.
The correct taxonomy term in the screenshot is the right-side one (slug: "test-si")

This happens when the taxonomy term has UI Mode set to Stack Selector in the collection blueprint:

How to reproduce

Here is the GitHub repo with the bug: https://github.com/andrazperson/statamic-taxonomy-localization-bug

Login credentials are:

• email: admin@example.com
• password: admin

To reproduce:

• link the taxonomy Categories to the Article blueprint and select it when creating a new entry in the Articles collection
• publish the entry on both Statamic EN and Statamic SI sites
• in the collection entries API response both entries should have a "Statamic EN" taxonomy term linked (incorrect), instead of EN taxonomy to EN site and SI taxonomy to SI site (correct)

Logs

No response

Environment

Environment
Application Name: Statamic
Laravel Version: 11.37.0
PHP Version: 8.3.11
Composer Version: 2.7.9
Environment: local
Debug Mode: ENABLED
URL: statamic-taxonomy-localization-bug.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

Statamic
Addons: 0
Sites: 2 (Statamic EN, Statamic SI)
Stache Watcher: Enabled (auto)
Static Caching: Disabled
Version: 5.45.1 PRO

Installation

Fresh statamic/statamic site via CLI

Additional details

No response