I'm trying to install an App from the Office Store in Office 365 Home Premium, specifically the online version accessed via OneDrive. Example of such an App would be Modern Trend for Excel. The documentation says click Insert > My Apps, but I don't find this menu option in the online Excel.
Can Apps be installed in the online version of Office? If so, how?
I doubt your question is suitable for SO as it seems you're asking about how to install an already made application as opposed to developing said applications.
In the event I'm incorrect...
Apparently not; that doesn't surprise me though. Also, notice the link you provided doesn't specify that it pertains to any of the online versions of mentioned programs.
I opened my account, created a blank worksheet, and tried to add an app. First thing to notice is that the ribbon is limited online. It doesn't even have the "Apps" section as shown in the link. So I proceeded to "open in Excel", which will open the file on your local machine. Yahtzee, I'm able to add the app.
Perhaps you should try adding the app at "home" and after opening the file online and see if the app is functional. Problem would be solved.