[FEATURE] Web project files panel: list view with front-end sorting and search

Preflight Checklist

• [X] I have searched existing requests and this feature hasn't been requested yet
• [X] This is a single feature request (not multiple features)

Problem Statement

The project files view on the web (the "Context" panel that lists a project's files, with a "Search files" modal and "Select a file to view its contents") only shows files as a two-column grid of squares. With around 50 files in a project, it gets really hard to find a file and change things. The only searchable list is inside the modal, so every lookup means opening it first.

Proposed Solution

1. A list view as well as the existing two-squares grid, with one row per file.
2. Ordering and sorting on that list, without having to open the modal. Do it in the front end on the files already loaded, so it adds no backend requests.
3. Search on that list as well.

Alternative Solutions

Opening the "Search files" modal each time. The search there works well, but it adds a step to every lookup.

Priority

High - Significant impact on productivity

Feature Category

Other

Use Case Example

1. I keep a project with about 50 files: dated reports (report-YYYY-MM-DD-HHMMSS.html) plus a plain-text copy of each.
2. I want to find the newest report, or pick out old ones to tidy up.
3. In the grid I scroll through squares. In a sortable list it takes one glance.

Additional Context

I'm filing this here because the web feedback button is in the Claude Code panel; I've also sent it through that button and through /feedback. I'm suggesting front-end sorting deliberately, so the feature costs no extra backend requests.