Deprecate the Search module

Problem/Motivation

Track the steps needed to deprecate extension Search from core to contrib. See Remove a core extension and move it to a contributed project of the deprecation policy.

The removal of extension Search was approved in #3476883: [Policy, no patch] Move Search module to contrib.

Remaining tasks

1. Create a section on Deprecated and obsolete modules and themes to provide recommendations for sites using extension Search. The recommendations are to include instructions for sites using the extension and for contributed projects that depend on then extension.
2. DONE. Add the following to the extension info.yml file

lifecycle: deprecated
lifecycle_link: https://www.drupal.org/node/3223395#s-search

3. DONE. Add #[IgnoreDeprecations] to all tests in the extension.
4. Add a change record and include a link the the doc page.
5. Deprecate any library that is only used by the extension.
6. Do a thorough search of core for any remaining references to the extension. If references are found, outside of the extension, then creates issues to remove the references.

Release notes snippet