bug(mat-tree): How to maintain tree expansion state if TreeControl is deprecated?

### Is this a regression?

- [x] Yes, this behavior used to work in the previous version

### The previous version in which this bug was not present was

pre v18.2.0

### Description

Previously, it was possible to maintain the expansion state independent of the MatTree (rendered) component by using a TreeControl.

With TreeControl deprecated, this does not appear possible any longer.

I rely on this feature so would appreciate consideration of a path forward.

Of note, the selection model is maintained privately in MatTree:
https://github.com/angular/components/blob/b961966d285c1f4986d214084ff585a713adc3bd/src/cdk/tree/tree.ts#L366-L372

Note that this is not a duplicate of #29856, which looks to relate to accessing some of the methods of TreeControl, which have been made available on MatTree itself.

### Reproduction

I can produce a reproduction but I believe the regression has been clearly explained above and a reproduction does not add value.

### Expected Behavior

There is a mechanism for maintaining expansion state independent of the rendered component.

### Actual Behavior

Expansion state is lost when the component is destroyed.

### Environment

```
Angular CLI: 18.0.3
Node: 18.20.5
Package Manager: npm 10.8.2
OS: darwin arm64

Angular: 18.0.2
... animations, common, compiler, compiler-cli, core, forms
... language-service, platform-browser, platform-browser-dynamic
... router

Package Version
-----------------------------------------------------------
@angular-devkit/architect 0.1800.3
@angular-devkit/build-angular 18.0.3
@angular-devkit/core 18.0.3
@angular-devkit/schematics 18.0.3
@angular/cdk 18.2.14
@angular/cli 18.0.3
@angular/flex-layout 14.0.0-beta.41
@angular/material 18.2.14
@angular/material-luxon-adapter 18.2.14
@schematics/angular 18.0.3
ng-packagr 18.0.0
rxjs 7.8.1
typescript 5.4.5
zone.js 0.14.4
```

Start with src/cdk/tree/tree.ts, especially the private selection model referenced in the issue, and trace how MatTree and the deprecated TreeControl manage expansion. Determine an API or state mechanism that preserves expansion independently of the rendered component. Done means expansion state survives component destruction and is covered by the relevant tree behavior tests.

Written by the indexing model from the issue text.