Fix lint errors and engine versions

[jguhlin]

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• Issue Linked: This PR is linked to an approved GitHub Issue (see "Related GitHub Issue" above).
• Scope: My changes are focused on the linked issue (one major feature/fix per PR).
• Self-Review: I have performed a thorough self-review of my code.
• Testing: New and/or updated tests have been added to cover my changes (if applicable).
• Documentation Impact: I have considered if my changes require documentation updates (see "Documentation Updates" section below).
• Contribution Guidelines: I have read and agree to the Contributor Guidelines.

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Important

Add LLM conversation saving feature, update engine versions, and enhance experimental settings and tests.

• Features:
  • Add LLM conversation saving feature in conversation-saver.ts.
  • Implement saveConversation() method to save conversations as JSON files.
  • Add getWorkspaceRoot() in index.ts to determine workspace root.
• Experiments:
  • Add llmConversationSaving to experimentIds in experiment.ts and experiments.ts.
  • Update experimentsSchema in experiment.ts to include llmConversationSaving.
  • Add configuration for llmConversationSaving in experimentConfigsMap in experiments.ts.
• UI:
  • Add UI controls for enabling LLM conversation saving in ExperimentalSettings.tsx.
  • Update settings.json to include descriptions for LLM_CONVERSATION_SAVING.
• Tests:
  • Update experiments.spec.ts and ExtensionStateContext.spec.tsx to test llmConversationSaving.
• Misc:
  • Change Node engine version in package.json to >=20.19.2.
  • Add @types/node and @types/vscode to devDependencies in package.json.

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