That definitely sounds like a conflict between the AdSense script and NodeBB's service worker registration. You could try lazy-loading the AdSense JS or excluding it from the scope of the service worker

This was caused by data-ad-format being set to auto on the widget html, this causes google js to add height:auto!important to all the parent element chain. Removing data-ad-format fixes it. I've added some widget options so it's value can be changed.

Theoretically, I found a workaround: disable advertisements only on the chat page. Can anybody tell me, how can I achieve this via custom code snippet and/or extension?

Twissell This usually happens when AdSense injects scripts before NodeBB finishes loading its own client files. The service worker fails to register and chat breaks for logged-in users. Try limiting AdSense to guests only or exclude the chat route from the plugin. If the problem disappears, you can report it to the plugin author to adjust the script order so it doesn’t block NodeBB’s core JS.