Extract package errors alert to separate component

What does this MR do and why?

Extract package errors alert to separate component

The feature is continuation of Improves alert message when multiple error pack... (!151550 - merged)

The code is extracted into separate component in preparation for #460583 (closed) with some UI text changed.

The final version would end up looking like Draft: Show accurate number of errored packages... (!169735 - closed)

MR acceptance checklist

Please evaluate this MR against the MR acceptance checklist. It helps you analyze changes to reduce risks in quality, performance, reliability, security, and maintainability.

Screenshots or screen recordings

Same as !151550 (merged)

How to set up and validate locally

Same steps can be followed

Related to #460583 (closed)