feat: add badge tracking to leaderboard sync and user api endpoint

[Yashaswini-K-P]

Description

This PR introduces an automated student badge tracking and calculation engine (SPEEDRUN, HOT_STREAK, UP_LINK) into the daily leaderboard synchronization cycle. It updates the user info API utility to cleanly parse and serve these newly generated badge mappings over the network to the frontend dashboard.

Linked Issue

Fixes #108

• scripts/sync-leaderboard.js: Built synchronous badge assignment steps, daily streak threshold algorithms, ranking delta trackers, and implemented safe atomicWrite file swaps to protect badges.json against file corruption.
• scripts/fetch-user-info.js: Updated the pipeline to request badges.json independently via separate, non-blocking try/catch HTTP blocks to dynamically deliver student badge matrices to the client interface.

Type of Change

• Bug fix
• New feature
• UI/Visual update
• Documentation update
• Refactor

Testing

• Tested locally
• Tested on mobile viewport (if applicable)
• No console errors introduced

Checklist

• My code follows the project's coding style
• I have formatted my code locally by running npx prettier --write . before submitting
• I am submitting my PR from a dedicated feature/* branch, not the main branch
• I have performed a self-review of my code
• My changes generate no new warnings or errors
• I have updated documentation if required
• I have linked the relevant issue

Screenshots / Screen Recording

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[jagdish-15]

Suggested change

	if (history.length >= 7) {
	const recentHistory = history.slice(-7);
	if (history.length >= 8) {
	const recentHistory = history.slice(-8);

We'd actually need 8 days of data here, similar to how we'd need data from yesterday to check if the user has solved a problem today