Angular: mat-button-toggle deselect selected after cancel dialog box

Question

I am having a problem with automatically deselecting a chosen mat-button-toggle if the cancel option is chosen in the dialog popup.

I made a dummy example from some angular code to demonstrate what I mean https://stackblitz.com/edit/angular-azhbe2?file=src/app/dialog-content-example.html

For example:

1. The Permanent field is selected at first
2. The Freelancer field is selected and a dialog opens, if "install" is chosen then the Freelancer field should still be the selected field -- but -- if the "cancel" option is chosen or it the dialog box is closed by clicking outside of the box, then the Permanent field should be chosen automatically again, not the Freelancer field..

Any ideas on how to handle this? Thanks :-)