I've looked through the API documentation https://contentful.github.io/contentful-management.js/contentful-management/11.51.0/ the published documentation for the Entries API https://www.contentful.com/developers/docs/references/content-management-api/#/reference/entries/entry a docs page on filtering API queries https://www.contentful.com/developers/docs/concepts/relational-queries/ the typescript definitions for the API and the draft "improve docs" PR but I can't find anything on how to get an entry based on its field values.
In particular, the content mangement API docs don't seem to say anything about the query object. The delivery API docs do, but it's also very incomplete, and the examples all say "No snippet for this SDK." for the Javascript Plain API