We are having problems publishing reports to workspaces from power bi desktop and updating/publishing apps on Power BI Web today (CEST time zone).
Yesterday everything worked fine, but today I just see a box which reads Publishing app. and the "spinning dots"!
As usual it is very important to publish the reports to web for those who need and use them in their daily work. Hope MS can fix it or suggest some kind of work around
From the first screenshot, the issue is happening when publishing the report from Power BI desktop to Power BI service. I would suggest you test again. Also you can go to Power BI service, click on Get Data -> Files to publish the report.
From the second screenshot, the issue is happening when publishing the app in Power BI service. It's a known issue listed in Support site, see:
Best Regards,Qiuyun Yu