chore: Remove deprecated state derivation functions from next (#6611)

## Explanation

The two deprecated state derivation functions (`getAnonymizedState` and
`getPersistentState`) have been removed from the `next` export, which as
upcoming breaking changes. `deriveStateFromMetadata` remains the
recommended replacement.

## References

Closes #6610

## Checklist

- [x] I've updated the test suite for new or updated code as appropriate
- [x] I've updated documentation (JSDoc, Markdown, etc.) for new or
updated code as appropriate
- [x] I've communicated my changes to consumers by [updating changelogs
for packages I've
changed](https://github.com/MetaMask/core/tree/main/docs/contributing.md#updating-changelogs),
highlighting breaking changes as necessary
- [x] I've prepared draft pull requests for clients and consumer
packages to resolve any breaking changes

Author: Gudahtt

eslint-warning-thresholds.json

@@ -110,7 +110,7 @@
     "import-x/namespace": 18
   },
   "packages/base-controller/src/next/BaseController.test.ts": {
-    "import-x/namespace": 18
+    "import-x/namespace": 14
   },
   "packages/build-utils/src/transforms/remove-fenced-code.test.ts": {
     "import-x/order": 1

packages/base-controller/CHANGELOG.md

@@ -12,6 +12,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Bump `@metamask/utils` from `^11.4.2` to `^11.8.0` ([#6588](https://github.com/MetaMask/core/pull/6588))
 - In experimental `next` export, rename `anonymous` metadata property to `includeInDebugSnapshot` ([#6593](https://github.com/MetaMask/core/pull/6593))
 - In experimental `next` export, make `includeInStateLogs` and `usedInUi` metadata properties required ([#6593](https://github.com/MetaMask/core/pull/6593))
+- In experimental `next` export, remove deprecated exports `getPersistentState` and `getAnonymizedState` ([#6611](https://github.com/MetaMask/core/pull/6611))
 
 ## [8.3.0]