The team has confirmed that an update will be published shortly. In the meantime, please continue using LanguageTool in WordPress. If you still encounter any issues after two weeks, don’t hesitate to reach out again—we’re here to help!
For the record, I am successfully using LanguageTool in a self-hosted WP installation. On the Brave browser, I had to select “Shields Down” by pressing on the orange logo near the URL field. Brave blocks about everything, which is exactly why I use it. Also, if you are using any sort of add blocking plugin or VPN, you may need to whitelist any page you want to use LanguageTool with. Good luck!