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/ai-providers.test.ts

@@ -0,0 +1,50 @@
+import { describe, expect, it } from "vitest"
+import { supportsImageInput, supportsPromptCaching } from "@/lib/ai-providers"
+
+describe("supportsPromptCaching", () => {
+    it("returns true for Claude models", () => {
+        expect(supportsPromptCaching("claude-sonnet-4-5")).toBe(true)
+        expect(supportsPromptCaching("anthropic.claude-3-5-sonnet")).toBe(true)
+        expect(supportsPromptCaching("us.anthropic.claude-3-5-sonnet")).toBe(
+            true,
+        )
+        expect(supportsPromptCaching("eu.anthropic.claude-3-5-sonnet")).toBe(
+            true,
+        )
+    })
+
+    it("returns false for non-Claude models", () => {
+        expect(supportsPromptCaching("gpt-4o")).toBe(false)
+        expect(supportsPromptCaching("gemini-pro")).toBe(false)
+        expect(supportsPromptCaching("deepseek-chat")).toBe(false)
+    })
+})
+
+describe("supportsImageInput", () => {
+    it("returns true for models with vision capability", () => {
+        expect(supportsImageInput("gpt-4-vision")).toBe(true)
+        expect(supportsImageInput("qwen-vl")).toBe(true)
+        expect(supportsImageInput("deepseek-vl")).toBe(true)
+    })
+
+    it("returns false for Kimi K2 models without vision", () => {
+        expect(supportsImageInput("kimi-k2")).toBe(false)
+        expect(supportsImageInput("moonshot/kimi-k2")).toBe(false)
+    })
+
+    it("returns false for DeepSeek text models", () => {
+        expect(supportsImageInput("deepseek-chat")).toBe(false)
+        expect(supportsImageInput("deepseek-coder")).toBe(false)
+    })
+
+    it("returns false for Qwen text models", () => {
+        expect(supportsImageInput("qwen-turbo")).toBe(false)
+        expect(supportsImageInput("qwen-plus")).toBe(false)
+    })
+
+    it("returns true for Claude and GPT models by default", () => {
+        expect(supportsImageInput("claude-sonnet-4-5")).toBe(true)
+        expect(supportsImageInput("gpt-4o")).toBe(true)
+        expect(supportsImageInput("gemini-pro")).toBe(true)
+    })
+})