Hi Volodymyr,
Greetings from Syncfusion support.
Upon reviewing your query, it appears that you are attempting to display
the Grid column chooser dialog by clicking an external button within a
Syncfusion dialog. We have created a sample that demonstrates a similar
scenario, where a button within a Syncfusion dialog component triggers the
opening of the Grid column chooser The column chooser dialog
now displays correctly over the Syncfusion dialog. You can refer to the
provided sample and the screenshot for further clarification.
Sample: https://stackblitz.com/edit/angular-jx5rvm-jzuvzz?file=src%2Fapp.component.html,src%2Fapp.component.ts
Screenshot:

If you
need any further assistance or have additional questions, please feel free to
let us know.
Regards,
Johnson Soundararajan S