[FEATURE] Web project files: delete button in the Search files modal

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 "Search files" modal in the web project files view (the project's "Context" panel) finds files well, but there's no way to delete a file from it. With around 50 files in a project, I can find the ones I want to remove, but I can't remove them where I found them.

Proposed Solution

A delete button for each file in the "Search files" modal.

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

Other

Use Case Example

1. My project holds about 50 dated report files, and older ones pile up.
2. I open "Search files", type a date prefix, and see the old reports.
3. I want to delete them right there.

Additional Context

This is filed separately from #98312 (list view with front-end sorting and search) so each request stays a single feature, as the template asks.