I've been playing around with this idea since I read the post yesterday. I did not come up with any solutions I'd consider using, but I'll give you the ideas I had partial success with. It might be enough for you. In the end, I'll tell you my own solution for this kind of thing. It's not really what you asked for, but it is my favorite way of keeping information together.
Most of the solutions I'll suggest depend on the fact there there is a web version of the App Store. It's not easy to get to using the more common web browsers on iPadOS, because most of them redirect to the App Store when they see a link to an app.
You can get the necessary web address by using Copy Link in the Share Sheed in the App Store
The first idea is the most flexible, but also the most work intensive. You copy the link from the App Store, then paste in into a third party browser that does not redirect to the App Store. Neither Safari nor Chrome will work. iCab Mobile works awkwardly, but works. It both redirects and displays the webpage. Initially it redirects you to the App Store, but if you go back to iCab Mobile and refresh the page it shows the website.
Once you have the website displayed in the browser you can copy and paste from the webpage. Like most website, it's not the best experience. Selecting content can be tricky. Selecting all content is tedious and doesn't result in great formatting when it is pasted.
Paste the content to your note, word-processor, or whatever of choice.
Second is similar, but instead you convert the app's webpage to a PDF. There are several ways to do this, but the easiest is to use a web to pdf converter. Once you have the PDF you can highlight and annotate it in a PDF editor or notation app like Notability.
As an experiment I used the free (with in-app purchase) app Web to PDF Converter & Reader by DIGISET LLC. To get the best results, I expanded the details before converting. The results were not bad. The only thing missing was the app's icon graphic.
Opening the PDF in Notability I can highlight text, add comments, place graphics and notes on top of the PDF, and add pages with more content. Notability isn't really a PDF annotation app, it's designed for students to take notes, often on top of PDF's (which are a common way for features to issue class materials). If you already have a decent PDF annotation app, it will probably do what you need.
This is the easiest method I came up with that more or less does what you asked. I still consider it too much work for return. But I'm lazy.
The third method is to use Shortcuts. This is the iOS iPadOS automation app. It lets you automate quite a few things. One of the commands, Get Details from App Store, can pull a fair amount of info for an app, like: Artist (developer), Name of app, Version, Description, Artwork. You could feasibly use this to gather information about an app and generate a PDF or text document.
I briefly fiddled with this, just enough to get an idea of how much work it would take. Not a lot, but more than I'm willing to put in for something I won't use. If you are going to be taking notes on apps as much as your post suggests, it might be worth your time to learn Shortcuts. The initial investment is large, but the payout would greatly reduce the work and time needed for this project.
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Finally, my own preferred way to do this kind of task. I use the Notes app.
In the case of Apps from the App Store, I use the Share Sheet to create a note for the app. This results in a rich link note with the App name as its title. I can zip right along in the App Store and make as many of these app notes as needed.
Next, I open the App Store side by side with the Notes app. Taping on the link in the Notes app will open the app's page in the App Store. The disadvantage is that I still can't copy/paste from the App Store. The advantage is that the information I do see is always up to date, not some out of date info I copied pasted.
I can then use the Notes apps to add any other information or comments I'd like. Things like: a bullet list of features I like, a table of pros and cons, links and or content from the developer's site. For the last I'd probably use the slide over version of Safari to browse and copy paste from the site. Or maybe I'd replace the App Store view with Safari if I was done with that portion of my editing.
I do similar things in Notes to comparison shop, gather info for projects, and create information notes for subjects.
Notes also lets you group notes into folders and subfolders for organization, which is handy when you have as many notes as I do.
It's a pretty versatile app.
Well, that was longer than I intended. I hope it gave you some useful Ideas.
