Can't input Japanese on `docusaurus-theme-search-algolia` in Windows Firefox

### Have you read the Contributing Guidelines on issues?

- [X] I have read the [Contributing Guidelines on issues](https://github.com/facebook/docusaurus/blob/main/CONTRIBUTING.md#issues).

### Prerequisites

- [X] I'm using the latest version of Docusaurus.
- [ ] I have tried the `npm run clear` or `yarn clear` command.
- [ ] I have tried `rm -rf node_modules yarn.lock package-lock.json` and re-installing packages.
- [ ] I have tried creating a repro with https://new.docusaurus.io.
- [ ] I have read the console error message carefully (if applicable).

### Description

`docusaurus-theme-search-algolia` has a bug to prevent from inputting Japanese in Windows Firefox.
Other languages, e.g. Chinese, may be affected, too.
Chromium-based browsers work well.

### Reproducible demo

https://docusaurus.io/

### Steps to reproduce

1. Install or enable a Japanese input method (e.g. Google Japanese Input)
2. Click the search bar or Ctrl + K
3. Enable Japanese input method
4. Type some Japanese search query

### Expected behavior

https://user-images.githubusercontent.com/12870451/235352380-d6be7c95-c69b-489d-b8eb-d00d5ecdc499.mp4

(Edge)

Chrome also works well.

Note: this movie uses AV1. Safari may not be supported. Edge requires an [this Windows video extension](https://www.microsoft.com/store/productId/9MVZQVXJBQ9V).

### Actual behavior

https://user-images.githubusercontent.com/12870451/235352442-ccfbda41-a997-463d-8d56-26a10a3fd361.mp4

Input corrupted at every moment😡

### Your environment

- Public source code: officia pagel
- Public site URL: official page
- Docusaurus version used: official
- Environment name and version (e.g. Chrome 89, Node.js 16.4): N/A
- Operating system and version (e.g. Ubuntu 20.04.2 LTS): Windows + Firefox

### Self-service

- [ ] I'd be willing to fix this bug myself.