test: reorganize flat test files into purpose-based subdirectories (phase 6)

Group 245 flat integration tests and 25 loose unit tests into
discoverable subdirectories per spec section 6:

  integration/tools/{image,video,audio,document,data}/  (156 files)
  integration/platform/                                  (64 files)
  integration/generated/                                 (14 files)
  integration/security/                                  (10 files)

  unit/security/     (8 files, new subdir)
  unit/api/          (7 files moved in)
  unit/web/          (3 files moved in)
  unit/shared/       (6 files moved in)
  unit/image-engine/ (1 file moved in)

All moves via git mv (history preserved). Relative imports repaired
for both depth levels (platform/generated/security = +1, tools/ = +2):
static from-imports, dynamic import() calls, vi.mock() paths,
import.meta.dirname joins, and __dirname joins.

Vitest discovery unchanged (no test.include in config, recursive glob
matches subdirs, shard-by-hash unaffected). test-server.ts and
tool-route-drift.test.ts stay at integration root. fixtures/ untouched.

Parity gate: 13189 passing test names before = 13189 after (0 dropped).

tests/unit/api/beautify-backgrounds.test.ts

@@ -0,0 +1,129 @@
+import sharp from "sharp";
+import { describe, expect, it } from "vitest";
+import {
+  generateBackground,
+  getDominantBackground,
+} from "../../../apps/api/src/lib/beautify/backgrounds.js";
+
+describe("generateBackground", () => {
+  it("generates a solid color background", async () => {
+    const buf = await generateBackground({
+      type: "solid",
+      color: "#ff0000",
+      width: 200,
+      height: 100,
+    });
+    const meta = await sharp(buf).metadata();
+    expect(meta.width).toBe(200);
+    expect(meta.height).toBe(100);
+    expect(meta.channels).toBe(4);
+  });
+
+  it("generates a linear gradient background", async () => {
+    const buf = await generateBackground({
+      type: "linear-gradient",
+      stops: [
+        { color: "#667eea", position: 0 },
+        { color: "#764ba2", position: 100 },
+      ],
+      angle: 135,
+      width: 400,
+      height: 300,
+    });
+    const meta = await sharp(buf).metadata();
+    expect(meta.width).toBe(400);
+    expect(meta.height).toBe(300);
+  });
+
+  it("generates a radial gradient background", async () => {
+    const buf = await generateBackground({
+      type: "radial-gradient",
+      stops: [
+        { color: "#667eea", position: 0 },
+        { color: "#764ba2", position: 100 },
+      ],
+      width: 400,
+      height: 300,
+    });
+    const meta = await sharp(buf).metadata();
+    expect(meta.width).toBe(400);
+    expect(meta.height).toBe(300);
+  });
+
+  it("generates a transparent background", async () => {
+    const buf = await generateBackground({
+      type: "transparent",
+      width: 200,
+      height: 100,
+    });
+    const meta = await sharp(buf).metadata();
+    expect(meta.width).toBe(200);
+    expect(meta.height).toBe(100);
+    expect(meta.hasAlpha).toBe(true);
+  });
+
+  it("generates an image background", async () => {
+    const red = await sharp({
+      create: {
+        width: 800,
+        height: 600,
+        channels: 4,
+        background: { r: 255, g: 0, b: 0, alpha: 1 },
+      },
+    })
+      .png()
+      .toBuffer();
+
+    const buf = await generateBackground({
+      type: "image",
+      imageBuffer: red,
+      width: 400,
+      height: 300,
+    });
+    const meta = await sharp(buf).metadata();
+    expect(meta.width).toBe(400);
+    expect(meta.height).toBe(300);
+  });
+
+  it("generates multi-stop linear gradient", async () => {
+    const buf = await generateBackground({
+      type: "linear-gradient",
+      stops: [
+        { color: "#0f0c29", position: 0 },
+        { color: "#302b63", position: 50 },
+        { color: "#24243e", position: 100 },
+      ],
+      angle: 135,
+      width: 400,
+      height: 300,
+    });
+    const meta = await sharp(buf).metadata();
+    expect(meta.width).toBe(400);
+    expect(meta.height).toBe(300);
+  });
+});
+
+describe("getDominantBackground", () => {
+  it("returns solid color for solid type", () => {
+    const result = getDominantBackground({ type: "solid", color: "#ff0000" });
+    expect(result).toEqual({ r: 255, g: 0, b: 0, alpha: 1 });
+  });
+
+  it("returns last gradient stop for gradient type", () => {
+    const result = getDominantBackground({
+      type: "linear-gradient",
+      stops: [
+        { color: "#667eea", position: 0 },
+        { color: "#764ba2", position: 100 },
+      ],
+    });
+    expect(result.r).toBe(118);
+    expect(result.g).toBe(75);
+    expect(result.b).toBe(162);
+  });
+
+  it("returns transparent for transparent type", () => {
+    const result = getDominantBackground({ type: "transparent" });
+    expect(result.alpha).toBe(0);
+  });
+});