Dear users, I'd like to share what the root cause was in my case.
It depends on the Communications Content Storage Location (https://support.zoom.us/hc/en-us/articles/360050781131)
We had it set to Germany and we had the issue. As soon as I set it to United States the issue disappeared. This is applicable irrespective of the fact we are recording the meeting or not: if we move browser users to break-out room and the Communications Content Storage Location is set to Germany we have the issue. Zoom engineering is working to fix it but meanwhile just changing to USA avoided the issue.
Hope this helps you as well!