New brand caduceus (vector mark, cyan #08EBF1->#3889FD) on a radial-depth navy
badge. Favicon family regenerated (svg/ico/png/apple-touch). Titlebar and
empty-state logos now use the self-contained navy badge so they render correctly
on every theme (light + dark) without washing out. Removed 5 per-skin CSS rules
that force-filled the titlebar icon to a flat accent color (they assumed the old
monochrome caduceus).
Squash-merges PR #613. Adds favicon to the app (was missing entirely — blank tab icon). 1371 tests passing, QA harness green. Review by independent agent (see PR comments). Follow-up commit addresses all three reviewer notes: hoisted _STATIC_MIME to module scope, fixed charset=utf-8 being appended to binary MIME types, confirmed correct MIME types on all three favicon formats.
Co-authored-by: tiansiyuan <tiansiyuan@users.noreply.github.com>