[STG-2002] feat: migrate Convex Stagehand package (#73)

* feat: migrate convex stagehand package

* fix: use trusted publishing compatible node

* chore: label release node version

Author: shrey150

.changeset/convex-stagehand-migration.md

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+---
+"@browserbasehq/convex-stagehand": patch
+---
+
+Migrate the Convex Stagehand package into the integrations monorepo.

packages/convex-stagehand/.prettierrc.json

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+{
+  "trailingComma": "all"
+}

packages/convex-stagehand/CHANGELOG.md

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+# @browserbasehq/convex-stagehand
+
+## 0.1.0
+
+### Minor Changes
+
+- [#11](https://github.com/browserbase/convex-stagehand/pull/11) [`ae8018e`](https://github.com/browserbase/convex-stagehand/commit/ae8018ef9188fff6bc221cc538fd2b832ec59c7d) Thanks [@shrey150](https://github.com/shrey150)! - Fix region handling for Stagehand sessions by persisting session region metadata and routing follow-up API calls to the correct regional Stagehand endpoint.
+  - Store `region` on session metadata and resolve region internally for `extract`, `act`, `observe`, `agent`, and `endSession`.
+  - Retry once on region-mismatch errors by parsing the returned region and updating metadata.
+  - Keep operation request payloads aligned with Stagehand API docs (region is not sent in operation bodies).
+  - Tighten internal TypeScript typing for region-aware API routing.
+
+## 0.0.3
+
+### Patch Changes
+
+- [#9](https://github.com/browserbase/convex-stagehand/pull/9) [`32b6e70`](https://github.com/browserbase/convex-stagehand/commit/32b6e705e534984935a231857810d98e1f89f97a) Thanks [@victlue](https://github.com/victlue)! - Strictly type BrowserbaseSessionCreateParams to match the Stagehand API spec, removing index signature backdoors
+
+## 0.0.2
+
+### Patch Changes
+
+- [#7](https://github.com/browserbase/convex-stagehand/pull/7) [`3ab9545`](https://github.com/browserbase/convex-stagehand/commit/3ab95452b00bd331ab170c26e0abc9888a099be9) Thanks [@shrey150](https://github.com/shrey150)! - Fix agent endpoint URL typo causing 404 errors. The agentExecute function was calling `/sessions/{id}/agent/execute` but the correct Stagehand API endpoint is `/sessions/{id}/agentExecute`. This fixes the `stagehand.agent()` function which was previously broken.
+
+- [#3](https://github.com/browserbase/convex-stagehand/pull/3) [`14db9a8`](https://github.com/browserbase/convex-stagehand/commit/14db9a81c53d02300adbd0d19454c1c85fee9e1e) Thanks [@shrey150](https://github.com/shrey150)! - Fix ComponentApi type to eliminate type assertion requirement. The ComponentApi type now correctly specifies "internal" visibility for component functions, matching the types generated for consumers. Users no longer need to use `as unknown as ComponentApi` type assertion when initializing the Stagehand client.
+
+  **Before:**
+
+  ```typescript
+  const stagehand = new Stagehand(components.stagehand as unknown as ComponentApi, { ... });
+  ```
+
+  **After:**
+
+  ```typescript
+  const stagehand = new Stagehand(components.stagehand, { ... });
+  ```

packages/convex-stagehand/LICENSE

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+MIT License
+
+Copyright (c) 2025 Browserbase Inc.
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.