How to fix the Magento 2.4.5 Layered Navigation showing incorrect results issue?

After upgrading Magento to version 2.4.5 you can see the error: TypeError: Magento\Elasticsearch\Model\ResourceModel\Fulltext\Collection\SearchResultApplier::categoryProductByCustomSortOrder(): Argument #1 ($categoryId) must be of type int, array given

Moreover, in Magento 2.4.5, if you have "display out of stock items" enabled, the layered navigation will not work correctly.

This bug is related to recent Magento changes and affects custom extensions such as Amasty Improved Layered Navigation.

How to fix the Magento 2.4.5 issue with Layered Navigation?

Magento appears to fix this bug only in the next release, but you don't have to wait for them to fix it – we've developed a free fixpack so that you can handle the issue. 

If you are Amasty customer, you can fix this error by installing additional package from our private repository:

composer require amasty/module-mage-2.4.5-fix

But this case can be reproduced without our extension. This is why we made the package public.