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/utils.test.ts

@@ -0,0 +1,86 @@
+import { describe, expect, it } from "vitest"
+import { cn, isMxCellXmlComplete, wrapWithMxFile } from "@/lib/utils"
+
+describe("isMxCellXmlComplete", () => {
+    it("returns false for empty/null input", () => {
+        expect(isMxCellXmlComplete("")).toBe(false)
+        expect(isMxCellXmlComplete(null)).toBe(false)
+        expect(isMxCellXmlComplete(undefined)).toBe(false)
+    })
+
+    it("returns true for self-closing mxCell", () => {
+        const xml =
+            '<mxCell id="2" value="Hello" style="rounded=1;" vertex="1" parent="1"/>'
+        expect(isMxCellXmlComplete(xml)).toBe(true)
+    })
+
+    it("returns true for mxCell with closing tag", () => {
+        const xml = `<mxCell id="2" value="Hello" vertex="1" parent="1">
+            <mxGeometry x="100" y="100" width="120" height="60" as="geometry"/>
+        </mxCell>`
+        expect(isMxCellXmlComplete(xml)).toBe(true)
+    })
+
+    it("returns false for truncated mxCell", () => {
+        const xml =
+            '<mxCell id="2" value="Hello" style="rounded=1;" vertex="1" parent'
+        expect(isMxCellXmlComplete(xml)).toBe(false)
+    })
+
+    it("returns false for mxCell with unclosed geometry", () => {
+        const xml = `<mxCell id="2" value="Hello" vertex="1" parent="1">
+            <mxGeometry x="100" y="100" width="120"`
+        expect(isMxCellXmlComplete(xml)).toBe(false)
+    })
+
+    it("returns true for multiple complete mxCells", () => {
+        const xml = `<mxCell id="2" value="A" vertex="1" parent="1"/>
+            <mxCell id="3" value="B" vertex="1" parent="1"/>`
+        expect(isMxCellXmlComplete(xml)).toBe(true)
+    })
+})
+
+describe("wrapWithMxFile", () => {
+    it("wraps empty string with default structure", () => {
+        const result = wrapWithMxFile("")
+        expect(result).toContain("<mxfile>")
+        expect(result).toContain("<mxGraphModel>")
+        expect(result).toContain('<mxCell id="0"/>')
+        expect(result).toContain('<mxCell id="1" parent="0"/>')
+    })
+
+    it("wraps raw mxCell content", () => {
+        const xml = '<mxCell id="2" value="Hello"/>'
+        const result = wrapWithMxFile(xml)
+        expect(result).toContain("<mxfile>")
+        expect(result).toContain(xml)
+        expect(result).toContain("</mxfile>")
+    })
+
+    it("returns full mxfile unchanged", () => {
+        const fullXml =
+            '<mxfile><diagram name="Page-1"><mxGraphModel></mxGraphModel></diagram></mxfile>'
+        const result = wrapWithMxFile(fullXml)
+        expect(result).toBe(fullXml)
+    })
+
+    it("handles whitespace in input", () => {
+        const result = wrapWithMxFile("   ")
+        expect(result).toContain("<mxfile>")
+    })
+})
+
+describe("cn (class name utility)", () => {
+    it("merges class names", () => {
+        expect(cn("foo", "bar")).toBe("foo bar")
+    })
+
+    it("handles conditional classes", () => {
+        expect(cn("foo", false && "bar", "baz")).toBe("foo baz")
+    })
+
+    it("merges tailwind classes correctly", () => {
+        expect(cn("px-2", "px-4")).toBe("px-4")
+        expect(cn("text-red-500", "text-blue-500")).toBe("text-blue-500")
+    })
+})