To use your query outside Extended Search screen, you need to save it as a Jira filter.
Instructions
In the Extended Search screen:
Type you JQL query and press Search
Click on Save the query as a filter
Give the filter a name and confirm
The filter is now available in Jira and you can use it in board, dashboard gadgets, Jira service desk, automation etc.
Make sure to read more about managing and sharing of filters: https://jqlsearchextensions.atlassian.net/l/c/uStPnv0Y