Thanks for the screenshots and more information. I can reproduce this by embedding a Web AppBuilder dashboard app in a Map Series Story Map, and then viewing the result on a relatively small screen.
The Web AppBuilder app is setting its mobile layout (and thus mobile popups) based on the size of the container that it's in. It switches to mobile layout if that container is narrower than 600 pixels wide or shorter than 600 pixels tall. Because the header of a Map Series app takes up about 100px of height, this means an embedded Web AppBuilder app will display in mobile layout if your browser window is shorter than about 700px.
This isn't anything that Story Maps can control on our end -- it's entirely a function of Web AppBuilder.
It's weird that this just started happening recently -- I looked at the Web AppBuilder code, and the 600px breakpoint has been around for at least a year. MapSeries hasn't changed its formatting or sizing either. Did you recently get a different monitor, or change your monitor's settings? I ran across this question in GeoNet that seems related to what you're seeing: WAB pop-ups in mobile format on desktop browser
If nothing has changed on your end, there is a way to force your Web AppBuilder app to display in desktop mode at smaller screen sizes. When you enter the URL of your Web AppBuilder app into Map Series, you can add a url parameter to the end of the URL to change the 600px breakpoint to something smaller, like this:
https://[your-org].maps.arcgis.com/apps/webappviewer/index.html?id=[your-app-id]&mobileBreakPoint=40...
With the addition of &mobileBreakPoint=400, your embedded app will display in desktop mode all the way down to 400px high or 400px wide. If that's not small enough, make that 400 smaller.
But this will apply to all smaller screens -- so if a user is viewing your Map Series app on an actual mobile phone, they'll still get the desktop layout of the embedded Web AppBuilder.
Here is the Web AppBuilder documentation about this and other url parameters you can use with any Web AppBuilder app: Use URL parameters—Web AppBuilder for ArcGIS (Developer Edition) | ArcGIS for Developers