mat-tree should have a filtering feature

#### Feature request, or proposal:
Filtering through tree nodes is a very useful feature, especially to reduce the size of tree and finding out the desired node(s) quickly.

#### What is the expected behavior?
There should be an input box above mat-tree. As you enter the text, it will filter through the tree and renders the tree based on the content in the input box.

#### What is the current behavior?
Filtering feature is not available in mat-tree component.

Start by reviewing the mat-tree component and its current public behavior to understand how tree nodes are represented and rendered. Define the filtering interaction and confirm that entering text reduces the displayed tree to matching nodes before adding coverage for the expected behavior.

Written by the indexing model from the issue text.