refactor(stage-ui): extract provider-inference package for runtime-neutral definitions (#2444)

## Summary

Extract runtime-neutral provider definitions from `@proj-airi/stage-ui`
into a new `@proj-airi/provider-inference` package that runs in both
Node.js and browser without Vue/Pinia dependencies.

## What changed

- **New package** `packages/provider-inference/` — owns
`ProviderDefinition`, `ProviderRegistry`, validators, and all provider
modules (cloud + local)
- **Provider modules relocated** — ~45 providers moved from
`stage-ui/src/libs/providers/providers/` to
`provider-inference/src/providers/cloud/` and
`provider-inference/src/providers/local/`
- **Type decoupling** — `ProviderContext.t` changed from
`ComposerTranslation` (Vue) to generic `ProviderTranslator`, removing
the Vue dependency from core types
- **stage-ui types slimmed** — `types.ts` now re-exports from
`provider-inference` and only adds the Vue-specific `ProviderViews`
extension
- **validators/run.ts** — becomes a pass-through re-export
- **Registry** — portable `createProviderRegistry()` with deterministic
ordering and duplicate-id detection

## Verification

```bash
pnpm -F @proj-airi/provider-inference typecheck
pnpm -F @proj-airi/provider-inference test:node
pnpm -F @proj-airi/provider-inference test:browser
pnpm -F @proj-airi/provider-inference build
pnpm -F @proj-airi/stage-ui typecheck
pnpm -F @proj-airi/stage-web typecheck
pnpm -F @proj-airi/stage-tamagotchi typecheck
pnpm lint
```

## Why

Provider definitions were tightly coupled to Vue (`ComposerTranslation`,
`Component`), preventing reuse in non-Vue runtimes (Node.js services,
tests, future Electron backend). This extraction creates a clean
boundary: runtime-neutral definitions live in `provider-inference`,
while Vue/Pinia-specific concerns stay in `stage-ui`.

packages/stage-pages/package.json

@@ -27,6 +27,7 @@
     "@proj-airi/audio": "workspace:^",
     "@proj-airi/ccc": "workspace:*",
     "@proj-airi/i18n": "workspace:*",
+    "@proj-airi/provider-inference": "workspace:^",
     "@proj-airi/server-sdk": "workspace:*",
     "@proj-airi/stage-ui": "workspace:*",
     "@proj-airi/stage-ui-live2d": "workspace:*",

packages/stage-pages/src/pages/settings/providers/transcription/browser-web-speech-api.vue

@@ -1,6 +1,7 @@
 <script setup lang="ts">
 import type { RemovableRef } from '@vueuse/core'
 
+import { streamWebSpeechAPITranscription } from '@proj-airi/provider-inference'
 import { errorMessageFromValue } from '@proj-airi/stage-shared'
 import {
   Alert,
@@ -10,7 +11,6 @@ import {
   ProviderSettingsLayout,
 } from '@proj-airi/stage-ui/components'
 import { selectProviderMetadata } from '@proj-airi/stage-ui/libs'
-import { streamWebSpeechAPITranscription } from '@proj-airi/stage-ui/libs/providers/providers/browser-web-speech-api'
 import { useProviderConfigStore } from '@proj-airi/stage-ui/stores/providers/config'
 import { useProviderStore } from '@proj-airi/stage-ui/stores/providers/provider'
 import { useSettingsAudioDevice } from '@proj-airi/stage-ui/stores/settings'