There are no basic tools to modify the global search results in the application. However, you can edit a schema that is responsible for the displaying the found data taken from a particular object according to your needs. You can modify the diff part of the code in the inherited from the object schema located in a Custom package. For accounts it is AccountSearchRowSchema and for contacts - ContactSearchRowSchema.
Clicking to the "Custom" section and adding a module gives me a selection of a lot of possibilities .... which one do i have to select? And why? The explanation in the manual is not very helpful for me.
It is absolutely expected behavior for the "GlobalSearchResult" page.
By default, ElasticSearch (the Global Search Service integrates ElasticSearch with Creatio) will index only sections regardless of their author, as well as string and lookup columns.
More information here: https://academy.creatio.com/docs/user/on_site_deployment/containerized_…
The "BirthDate" column is a date type, so you don't see this column on the "GlobalSearchResult" page.