Paint every floating service plate from one mixin

The auth flow's corner buttons and the empty column's tip toggle and nav pills
are the same plate — the service-message colour, white ink, and a hover shade
that has to be composed from the colour's own parts because
`--message-highlighting-hover-color` is declared on `.chat` and none of these
sit inside one. Each had written that out for itself; `service-plate()` now
holds it and they include it. The emitted CSS is unchanged.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>