Rewrite Bigtest tests for Search component with jest/react-testing-library

Purpose:
Rewrite tests for Search component with jest/react-testing-library.

Acceptance criteria:
1. Tests are written and the coverage above 80% is reached (according to the note below in order to prove it the screenshot should be attached in JIRA comment);

Note: that Bigtest tests should not be removed for a while. The reason for this is that there is no way right now to see metrics for Bigtest tests run and jest/rtl tests run separately. Once it is done we can start removing Bigtest tests when there are replacement tests written with jest/rtl.