An auto-updating sheet based on another sheet's data?

What I'm requesting is quite convoluted, I'll admit, but this is what I'd like to do for a spreadsheet of my belongings to organize during a big move:

I'd like to have one sheet (Sheet 1) that has a multiple columns with different lists of items (electronics, figures, etc), and next to these columns another column that dictates which box that item will be inside (box MG01, box CW01, etc). The second sheet (Sheet 2) will have all the boxes in columns, and each box column will look at Sheet 1 and copy down only the items that have the corresponding box.

If I update which box the item is in in Sheet 1, it just disappears from the previous box column in Sheet 2 and reappears in the column for the updated box. The box columns in Sheet 2 get rearranged so there's no randomly empty cells in them

Example sheet (in Google Sheets because it's easier to share but if the solution uses an Excel-only tool/feature I can switch to my Excel file)

I know I might be asking for a lot, but if there's a script or an extra sheet that needs to be created for organization purposes I'm ok with adding that step.

Thank you all!