Changes

landing: modal registration, value-led proof band, autocomplete fix, APK live

- Registration moved into a native <dialog> modal driven from every CTA, with
  focus trap/return, scroll lock, backdrop + ESC dismissal, full-screen sheet on
  mobile and prefers-reduced-motion respected.
- Replaced the data-source stats ("Quelle: Bundes-Klinik-Atlas", 293, 906) with
  three statements of what the product actually does. No invented metrics: the
  only figure left is the real 1.581 Klinik-Atlas count that was already there.
- Fixed the autocomplete staying open after a clinic was picked. Root cause was
  watch(query): selecting wrote the label back into the field, which the watcher
  read as a new search and reopened the list ~220ms later. The input is now
  :value + @input so a programmatic write cannot be a search intent, with a
  pendingQuery flag gating every path that opens the list.
- Removed Anrede end-to-end. The DB column is deliberately NOT migrated: it keeps
  its NOT NULL DEFAULT '' so inserts that omit it stay valid on existing databases.
- Android badge switched live: the APK is published at
  https://blut24.com/downloads/blut24-mobile.apk and served from disk by nginx
  with the correct package MIME type.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
 (commit: 9d95707)