arun-v-p/StudyDesk ? reverse-engineered prompt

Build me a local first study planner web app called StudyDesk that feels fast and works offline once it loads.

I want one place for tasks, deadlines, a weekly timetable, a month calendar, pinned notes, a Pomodoro focus timer, and revision plans. The app should open with a simple today view that shows what is due, what classes are happening today, and a quick progress ring. It should let me add, edit, search, filter, and complete items easily, and make the calendar and timetable feel really clear and visual.

Please make local storage the default, with no account needed for normal use, and add an optional cloud sync sign in for people who want it. Include backup and restore, import and export for calendar files and study resources, and make sure data stays private by default. I also want it to be installable as a PWA, with a clean modern UI, keyboard shortcuts, and good accessibility. If you need to check current docs for any integrations, look them up online first.