[Bug] HOT_STREAK/HARD_CARRY badges count non-consecutive recorded days as consecutive

[vedant7007]

Problem

frontend/js/user/badges.js (~lines 36-81) recomputes a "streak" by walking the last 8 recorded history entries and incrementing whenever total[j] - total[j-1] >= 1, with no calendar-day validation.

Impact (correctness)

History entries only exist for days a sync actually ran, so gaps are normal. A user active on 8 non-consecutive recorded days (which can span weeks) earns HOT_STREAK, titled "Solved ≥1 problem every day for 7 days." HARD_CARRY (~lines 75-81) has the same flaw over its 7-entry window regardless of calendar span. The code also ignores the backend streak object that fetch-user-info.js already returns.

Suggested fix (small)

Validate consecutive calendar days between adjacent entries (mirror the diffDays === 1 logic in scripts/backfill-streaks.js:30-38), or drive the badge from the backend data.streak field.

Related to #360/#196 (wiring the streak card to backend), but this is a distinct mis-count in the badge logic itself.

Happy to fix under GSSoC '26 if assigned.

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[jagdish-15]

This is essentially covered by #360, which is actively in progress and replaces the entire history-walk logic with data.streak.current >= 7.

As for the calendar-gap concern, our sync is designed to run on a regular cron schedule, so history entries are expected to be written consistently. While a missing day would be an infrastructure issue rather than a badge logic issue, #360 removes the history-walk implementation entirely anyway.

Closing as a duplicate of #360.