Misc: Mobile UI

### Summary
The current UI isn't very good on mobile devices. We should start thinking about how we can improve it.

### Possible solutions
There are two paths we could go down:
1. Create an entirely separate UI for mobile devices
2. Make modifications to the current UI so that it adjusts better to fit smaller screens

I'm keen to hear people's opinions on which route they think is best. There are definitely pros and cons to each one. If we create an entirely new UI, it will break a lot of the code in `src/web/` which is currently tightly coupled to the existing DOM. However, modifying the current UI to work better on mobile could result in messy code if it isn't done well. This could be a good time to start building `index.html` in a more modular fashion so that the code becomes easier to maintain.

If anyone wants to mock up some designs for what a mobile UI could look like, please go ahead. The focus should be on simplicity.

Review src/web/ and index.html first, then inspect the open linked pull request to understand the current work. The issue does not define a chosen mobile approach, target screens, or acceptance criteria, so “done” requires agreeing on the direction and scope before implementation.

Written by the indexing model from the issue text.