Move the Khanmigo data functions to Perseus Core for Server Side Scoring initiative (#3091)

## Summary:
This PR moves `getAnswersFromWidget`, `injectWidgets`, and a handful of helper functions to Perseus Core so that they are available for the Perseus service. We will be creating a new API endpoint to call these functions, so that we can support Khanmigo's move to keeping answerful data server-side.

It also created the new `getPerseusAIData` function, which will be used for the new API Endpoint. 

**I'm happy to take any direction on the name**, as "getPromptJSON" didn't feel the most descriptive or correct to myself or the AI team. I don't feel like I've nailed the perfect name either, but it seemed clearer at least. 

Issue: LEMS-3766

## Test plan:
- Tests pass
- Tests pass upstream
- Integration works upstream

Author: SonicScrewdriver

Reviewers: SonicScrewdriver, handeyeco, jeremywiebe, benchristel

Required Reviewers:

Approved By: handeyeco

Checks: ⏭️  1 check has been skipped, ✅ 10 checks were successful

Pull Request URL: #3091

Author: SonicScrewdriver

.changeset/nasty-teachers-retire.md

@@ -0,0 +1,6 @@
+---
+"@khanacademy/perseus": minor
+"@khanacademy/perseus-core": minor
+---
+
+Move the Khanmigo data functions to Perseus Core for Server Side Scoring initiative

packages/perseus-core/src/index.ts

@@ -217,6 +217,12 @@ export {
 } from "./utils/generators/image-widget-generator";
 export {generateVideoWidget} from "./utils/generators/video-widget-generator";
 
+export {
+    getAnswersFromWidgets,
+    injectWidgets,
+    getPerseusAIData,
+} from "./utils/extract-perseus-ai-data";
+
 import {registerCoreWidgets} from "./widgets/core-widget-registry";
 
 registerCoreWidgets();