[Enhancement]: Use TSX and shadcn on the UI

[jonbarrow]

Checked Existing

• I have checked the repository for duplicate issues.

What enhancement would you like to see?

This suppliments #27, which is about design rather than implementation. This request is about implementation rather than design.

With the move to TypeScript in #26, we should consider moving the UI to using TSX rather than raw html. We do not necesarily need a full blown framework like React however, though of course one could be used. I suggest using shadcn since it's framework-agnostic, and even works without a framework like React at all through it's manual setup guide. This makes it a great choice for us since we don't have to worry about which framework we use, if any, and we do not have to make these components ourselves. It even ships with components for things relatively annoying to do by hand, such as multiple resizable panels.

I'm going to tag @wolfendale in this since he showed interest in helping out on the UI side of the rewrite

Any other details to share? (OPTIONAL)

Unless #26 is merged, any changes related to this issue should target the rewrite branch.