feat(clients/gamepad-ui): section tabs, background palettes, and a backdrop that moves everywhere

The console settings were one 30-row scroll, which on a Deck meant thumbing past
Video and Audio to reach the pad settings. They are now split across sections —
Stream · Video · Audio · Controller · Interface · Profiles, plus Input on the
desktop console, which alone carries the touch/mouse rows. L1/R1 walks them,
each section remembers where its cursor was, and the names are the same word on
every client so a setting is where you looked for it last.

Shoulders are not the only route, because a D-pad remote hasn't got any: on
Android, Up from the first row moves onto the strip (left/right walks sections
there, A drops back in), and on tvOS the pills are focusable, so the focus
engine handles it — a Siri Remote has no extended gamepad profile and never
reaches the input poll at all. The desktop console needs neither; PageUp and
PageDown already map to the same events.

New "Background" row, six palettes: Violet (the brand default), Tide, Forest,
Ember, Rose, Graphite. A palette is a hue rotation plus a saturation scale over
the ONE colour field each client already draws, so every palette inherits its
structure and Violet is the identity transform — existing installs see exactly
what they see today. The maths is ported three times (Rust/Swift/Kotlin) under
one shared `ui_palette` key, with the same assertions pinned in each language.
It is presentation only, so it is a device preference and never part of a
profile.

The form screens no longer have a backdrop of their own. Settings, add-host and
pair used to sit on a still gradient; they now wear the same living field at a
calm mix — pools dimmed onto the palette's own corner colour, vignette halved so
rows that run to the edges don't get crushed. On the desktop console that
collapsed the old aurora-over-static crossfade into one shader pass with a
chased uniform. Motion speed is identical in both modes on purpose: changing it
would make the field jump mid-transition. Nothing in the gamepad UI is backed by
a static image now, and Reduce Motion (Apple) / "remove animations" (Android)
still freeze it.

Also: the settings screen had no raster coverage at all — the eyeball dump is
`#[ignore]`d — so a new test draws every tab, and the Android screenshot set
gains a console-settings scene. Both earned their keep immediately: the renders
showed the extra hint pushing "Done" off a 360 dp phone (the legend scrolls now,
and the Section cell only appears where shoulders exist) and the form backdrop
crushing its own edges.

crates/pf-console-ui/src/shell/render.rs

@@ -8,7 +8,7 @@ use crate::screens::{Bg, Ctx, Screen};
 use crate::theme::{white, Fonts, PanelStroke, W, WHITE};
 use pf_client_core::gamepad::PadInfo;
 use pf_client_core::trust;
-use skia_safe::{Canvas, Color4f, Rect};
+use skia_safe::{Canvas, Rect};
 use std::time::Instant;
 
 use super::{Motion, Shell, BOTTOM_BAND, TOP_BAND};
@@ -67,7 +67,9 @@ impl Shell {
             }
         };
 
-        // Backdrop crossfade follows the top screen.
+        // The backdrop settles into (or out of) calm with the screen transition. It is the
+        // SAME living field either way — a form screen quiets it, it doesn't replace it —
+        // so this is one shader pass with a chased uniform, not two stacked backdrops.
         let bg_target = match self.stack.last().expect("non-empty").background() {
             Bg::Aurora => 0.0,
             Bg::Form => 1.0,
@@ -76,16 +78,7 @@ impl Shell {
         if (self.bg_mix - bg_target).abs() < 0.005 {
             self.bg_mix = bg_target;
         }
-        if self.bg_mix < 1.0 {
-            self.draw_aurora(canvas, w, h, t);
-        } else {
-            canvas.clear(Color4f::new(0.0, 0.0, 0.0, 1.0));
-        }
-        if self.bg_mix > 0.0 {
-            canvas.save_layer_alpha_f(None, self.bg_mix as f32);
-            crate::theme::draw_form_background(canvas, w, h);
-            canvas.restore();
-        }
+        self.draw_aurora(canvas, w, h, t, self.bg_mix);
 
         // The screens, through the transition choreography.
         let content = Rect::from_ltrb(