feat: Add floating draggable Syllabus Miniplayer overlay

[Rithish-2914]

Description

This PR introduces a new global Syllabus Miniplayer to vastly improve the student user experience. Instead of forcing students to navigate away from the paper they are currently solving to check the syllabus, they can now view the syllabus in a floating picture-in-picture overlay.

Key Features

• Global Availability: The dock mounts on both the main Catalogue page and individual Paper views.
• Picture-in-Picture UX: Starts as an unobtrusive floating pill at the bottom right of the screen.
• Draggable & Resizable: Users can freely drag the panel anywhere on the screen and resize it from the corner. It automatically bounds-checks so it doesn't get lost off-screen.
• State Persistence: Cleanly resets position on hard refreshes to guarantee it never gets stuck out of bounds.
• Responsive: Scales beautifully and snaps to a full-screen sheet on mobile devices.
• Database Integrated: Added the syllabus field to the Course schema and created a new /api/syllabus route to fetch the live PDFs.

Visuals

WhatsApp.Video.2026-09-21.at.21.59.33.mp4