feat(plymouth): boot splash background follows the active palette

themes/engine/plymouth/nomarchy.script had
`Window.SetBackgroundTopColor(0.101, 0.105, 0.149)` hardcoded — a
Tokyo-Night-ish #1a1b26 — and nomarchy.plymouth had a matching
`ConsoleLogBackgroundColor=0x1a1b26`. Both were frozen regardless of
the active nomarchy.system.theme.

Replaced the literals with placeholders (@BG_R@, @BG_G@, @BG_B@,
@BG_HEX@) in the source files. themes/engine/plymouth.nix now reads
the active palette via `nomarchyLib.getPalette
config.nomarchy.system.theme`, converts palette.base00 into three
0.0–1.0 floats (Nix has no floating-point math, so `(byte * 1000) /
255` integer division formatted as `0.XXX`), and `sed`-substitutes
both files during installPhase.

Smoke-built the derivation against the default summer-night palette:

  $ cat .../nomarchy.script | grep BackgroundTopColor
  Window.SetBackgroundTopColor(0.176, 0.207, 0.231);
  $ cat .../nomarchy.plymouth | grep ConsoleLogBackgroundColor
  ConsoleLogBackgroundColor=0x2d353b

Both match the expected byte→float conversion from base00=2d353b.

Closes the "Plymouth theme variants per palette" Next-column item.
`nix flake check --no-build` clean.

themes/engine/plymouth.nix

@@ -1,6 +1,37 @@
 { config, pkgs, lib, ... }:
 
 let
+  nomarchyLib = import ../../lib { inherit lib; };
+  palette = nomarchyLib.getPalette config.nomarchy.system.theme;
+
+  # Plymouth's Window.SetBackgroundTopColor takes three floats in 0.0–1.0;
+  # the .plymouth metadata's ConsoleLogBackgroundColor takes a 0xRRGGBB
+  # hex. Compute both from palette.base00 so the boot splash matches the
+  # rest of the active theme instead of staying frozen on the hardcoded
+  # Tokyo-Night-ish #1a1b26 it used to ship with.
+  hex = palette.base00;
+  rByte = lib.fromHexString (lib.substring 0 2 hex);
+  gByte = lib.fromHexString (lib.substring 2 2 hex);
+  bByte = lib.fromHexString (lib.substring 4 2 hex);
+
+  # byte → "0.XXX" decimal string. Nix has no floating-point math, so
+  # multiply first, integer-divide, then format. Plymouth tolerates more
+  # decimals than this (0.1019 etc.) but three digits matches the visual
+  # precision Plymouth renders at and keeps the substitution readable.
+  byteToFloat = n:
+    let
+      thousandths = (n * 1000) / 255;
+      s = toString thousandths;
+      padded =
+        if lib.stringLength s == 1 then "00${s}"
+        else if lib.stringLength s == 2 then "0${s}"
+        else s;
+    in "0.${padded}";
+
+  bgR = byteToFloat rByte;
+  bgG = byteToFloat gByte;
+  bgB = byteToFloat bByte;
+
   nomarchy-plymouth = pkgs.stdenv.mkDerivation {
     pname = "nomarchy-plymouth";
     version = "1.0";
@@ -10,8 +41,21 @@ let
     installPhase = ''
       mkdir -p $out/share/plymouth/themes/nomarchy
       cp * $out/share/plymouth/themes/nomarchy/
+
       # Fix path in the plymouth file to point to the nix store
-      sed -i "s|/[a-z]*/share/plymouth/themes/nomarchy|$out/share/plymouth/themes/nomarchy|g" $out/share/plymouth/themes/nomarchy/nomarchy.plymouth
+      sed -i "s|/[a-z]*/share/plymouth/themes/nomarchy|$out/share/plymouth/themes/nomarchy|g" \
+        $out/share/plymouth/themes/nomarchy/nomarchy.plymouth
+
+      # Substitute the active theme's base00 in both the .script (RGB
+      # floats for the Window.SetBackground* calls) and the .plymouth
+      # metadata (0xRRGGBB for ConsoleLogBackgroundColor).
+      sed -i \
+        -e 's|@BG_R@|${bgR}|g' \
+        -e 's|@BG_G@|${bgG}|g' \
+        -e 's|@BG_B@|${bgB}|g' \
+        $out/share/plymouth/themes/nomarchy/nomarchy.script
+      sed -i 's|@BG_HEX@|${hex}|g' \
+        $out/share/plymouth/themes/nomarchy/nomarchy.plymouth
     '';
   };
 in