feat(web): add course register sidepanel

[xyspg]

📌 What's Changed

add side panel and handle courses alternatives. Closes #67 and #79

✅ Actions

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📝 Notes for Reviewer

the state between components becomes complex. should we setup a state management library

[chenxin-yan]

A few things to address:

• when user is trying to add a course that has a conflicting timeslot on calendar. Show a dialog to user to ask if want to add as alternative
• when handling "add as alternative" it gave user all the userCourseOfferings to select. However, we only want to scope to that year. For example, if I am planning for spring 2026, when I do not want to see courses I had for fall 2025 shown when adding alternatives
• If course A is an alternative of B, When B is deleted, A should be available. Currently, when B is deleted, A is also delete$
• user should be switching between alternative courses easily. I should be clicking on an courses that is an alternative and replace that with that it was alternative of.

[chenxin-yan]

looks great. I tested it locally and it works. I will look at the code later and clean things up if needed. The only thing is that, it seems to have performance issue with the side panel. Is it lagging when you use the seedling data?

[xyspg]

looks great. I tested it locally and it works. I will look at the code later and clean things up if needed. The only thing is that, it seems to have performance issue with the side panel. Is it lagging when you use the seedling data?

I will look into it. I was focusing on the interaction logic so I didn't notice the lag