Ask AI on docs doesn't work

### Describe the bug After very first question: <img width="887" height="175" alt="Image" src="https://github.com/user-attachments/assets/87a14361-f074-48f8-b4b7-15c26642a7c8" /> After second: <img width="922" height="175" alt="Image" src="https://github.com/user-attachments/assets/4282f0da-e030-4835-b2df-c413cae7375e" /> Reference: https://github.com/wxt-dev/wxt/discussions/2037 ### Reproduction 1. Visit [docs](https://wxt.dev/guide/installation.html) 2. Click "Ask AI" button on the right bottom 3. Type anything and submit ### Validations - [x] Read the [Contributing Guidelines](https://github.com/wxt-dev/wxt/blob/main/CONTRIBUTING.md). - [x] Read the [docs](https://wxt.dev/guide/installation.html). - [x] Check that there isn't [already an issue](https://github.com/wxt-dev/wxt/issues) that reports the same bug to avoid creating a duplicate. - [x] Check that this is a concrete bug. For Q&A open a [GitHub Discussion](https://github.com/wxt-dev/wxt/discussions) or join our [Discord Chat Server](https://discord.gg/ZFsZqGery9). - [x] The provided reproduction is a [minimal reproducible example](https://stackoverflow.com/help/minimal-reproducible-example) of the bug.