Implement a "copy query" button in the query input

Created by: lguychard

Figma design: https://www.figma.com/file/4Fy9rURbfF2bsl4BvYunUO/RFC-261-Search-Contexts?node-id=581%3A4754

Implement a copy query button in the search input (may reuse the existing, feature-flagged copy query button). Clicking the button will copy to the clipboard a string including:

• The contents of the search input
• The search context
• The pattern type
• If applicable, the case: filter