chore: include browser test for provider-inference package (#2446)

## Description

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about the "what" this PR is solving -->

## Linked Issues

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## Additional Context

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packages/provider-inference/vitest.config.ts

@@ -1,31 +1,33 @@
+import type { TestProjectInlineConfiguration } from 'vitest/config'
+
 import { playwright } from '@vitest/browser-playwright'
 import { defineConfig } from 'vitest/config'
 
+export const providerInferenceProjects: TestProjectInlineConfiguration[] = [
+  {
+    test: {
+      name: 'node',
+      include: ['src/**/*.test.ts'],
+      exclude: ['src/**/*.browser.test.ts'],
+    },
+  },
+  {
+    test: {
+      name: 'browser',
+      include: ['src/**/*.browser.test.ts'],
+      browser: {
+        enabled: true,
+        headless: true,
+        provider: playwright(),
+        instances: [{ browser: 'chromium' }],
+      },
+    },
+  },
+]
+
 export default defineConfig({
   root: import.meta.dirname,
   test: {
-    projects: [
-      {
-        extends: true,
-        test: {
-          name: 'node',
-          include: ['src/**/*.test.ts'],
-          exclude: ['src/**/*.browser.test.ts'],
-        },
-      },
-      {
-        extends: true,
-        test: {
-          name: 'browser',
-          include: ['src/**/*.browser.test.ts'],
-          browser: {
-            enabled: true,
-            headless: true,
-            provider: playwright(),
-            instances: [{ browser: 'chromium' }],
-          },
-        },
-      },
-    ],
+    projects: providerInferenceProjects,
   },
 })

vitest.config.ts

@@ -1,5 +1,7 @@
 import { defineConfig } from 'vitest/config'
 
+import { providerInferenceProjects } from './packages/provider-inference/vitest.config'
+
 export default defineConfig({
   test: {
     projects: [
@@ -18,7 +20,7 @@ export default defineConfig({
       'packages/better-ws',
       'packages/plugin-sdk',
       'packages/plugin-sdk-tamagotchi',
-      'packages/provider-inference',
+      ...providerInferenceProjects.map(project => ({ ...project, root: 'packages/provider-inference' })),
       'packages/scenarios-stage-tamagotchi-browser',
       'packages/scenarios-stage-tamagotchi-electron',
       'packages/server-runtime',