Add grouping to mat-table on Angular. Stackblitz provided.

This is an Angular 14 request, just need someone to combine two features into one stackblitz project.
You dont need to develop a new feature.

I have a mat-table with some filtering, I need to add a grouping feature that I found and its working in a separate stackblitz.
Just want to have the grouping feature on the mat-table with the filtering.

Stackblitz with filters: https://stackblitz.com/github/HalitTalha/mat-table-filter-example?file=src%2Fapp%2Fapp.component.ts
Stackblitz with grouping: https://stackblitz.com/edit/ag-mat-table-row-grouping?file=src%2Fapp%2Fapp.component.html,src%2Fapp%2Fapp.component.ts,src%2Fapp%2Fapp.module.ts

I want a merge of both