Based on my test in the IE browser, the dashboard in workspace has "Dark theme" still has "Dark theme" after publishing to App. You may try other browsers, and pay attention to the steps publishing to App, see more: Publish an app in Power BI.
Picture1: the dashboard in workspace has "Dark theme"
Picture2: when publish to App, the dashboard still has "Dark theme"
Community Support Team _ Amy
If this post helps, then please consider Accept it as the solution to help the other members find it more quickly.