test: add Vitest and Playwright testing infrastructure

- Add Vitest for unit tests (39 tests)
  - cached-responses.test.ts
  - ai-providers.test.ts
  - chat-helpers.test.ts
  - utils.test.ts
- Add Playwright for E2E tests (3 smoke tests)
  - Homepage load
  - Japanese locale
  - Settings dialog
- Add CI workflow (.github/workflows/test.yml)
- Add vitest.config.mts and playwright.config.ts
- Update .gitignore for test artifacts

tests/unit/cached-responses.test.ts

@@ -0,0 +1,54 @@
+import { describe, expect, it } from "vitest"
+import {
+    CACHED_EXAMPLE_RESPONSES,
+    findCachedResponse,
+} from "@/lib/cached-responses"
+
+describe("findCachedResponse", () => {
+    it("returns cached response for exact match without image", () => {
+        const result = findCachedResponse(
+            "Give me a **animated connector** diagram of transformer's architecture",
+            false,
+        )
+        expect(result).toBeDefined()
+        expect(result?.xml).toContain("Transformer Architecture")
+    })
+
+    it("returns cached response for exact match with image", () => {
+        const result = findCachedResponse("Replicate this in aws style", true)
+        expect(result).toBeDefined()
+        expect(result?.xml).toContain("AWS")
+    })
+
+    it("returns undefined for non-matching prompt", () => {
+        const result = findCachedResponse(
+            "random prompt that doesn't exist",
+            false,
+        )
+        expect(result).toBeUndefined()
+    })
+
+    it("returns undefined when hasImage doesn't match", () => {
+        // This prompt exists but requires hasImage=true
+        const result = findCachedResponse("Replicate this in aws style", false)
+        expect(result).toBeUndefined()
+    })
+
+    it("returns undefined for partial match", () => {
+        const result = findCachedResponse("Give me a diagram", false)
+        expect(result).toBeUndefined()
+    })
+
+    it("returns response for Draw a cat prompt", () => {
+        const result = findCachedResponse("Draw a cat for me", false)
+        expect(result).toBeDefined()
+        expect(result?.xml).toContain("ellipse")
+    })
+
+    it("all cached responses have non-empty xml", () => {
+        for (const response of CACHED_EXAMPLE_RESPONSES) {
+            expect(response.xml).not.toBe("")
+            expect(response.xml.length).toBeGreaterThan(0)
+        }
+    })
+})