I know it is technically possible to put the same application into the app store with 2 almost identical APKs (different package names and titles), although probably a bit d
You can if the package name of the app is different, as you said. This is done quite often for apps with trial and paid version. Regarding your question, we have right now around 6 apps in Google Play which are different branded versions of the same app. This means, they have their own package name, splash screen, and some database data, but the app is really the same. So far we didn't get any trouble with Google, so I would say it's possible.
Just for reference, in case you are interested in doing something similar, the best option in terms of maintainability of your app, consists in using an Android library project.
Basically you have one main big project with the "Android Library" option checked in Eclipse. You have all the main code there. On the other hand, you create two additional projects linked to your library. They will just need their manifest.xml and some activity to call the main activity of the library. Their package names must be different if you want to publish both apps in Google Play.
Additionally, you can override some resources for every project. For instance, you could have a boolean in /res/values indicating whether the project is a trial or paid version, with different values for them. Then, in the library you could check this boolean to show advertisements if it's a trial version. Another useful thing you can do is using a custom splash screen for every app, by having different image resources in every project with the same name.
As far as I know, it is allowed and certainly has been done in the past (malware masquerading as popular games). Provided the app you're publishing is your own work (and really only the name is different), then I can't see anyone reporting it either.
It is prohibited according to Play Console Developer Program Policy (effective October 21, 2020).
We don't allow apps that merely provide the same experience as other apps already on Google Play. Apps should provide value to users through the creation of unique content or services. Here are some examples of common violations: Copying content from other apps without adding any original content or value. Creating multiple apps with highly similar functionality, content, and user experience. If these apps are each small in content volume, developers should consider creating a single app that aggregates all the content.