Transfer apps from iPad/iPhone without a Mac

No. Apps can not be directly transferred between devices. For iOS/iPadOS, Apps can only be downloaded and installed from the Apple App Store.

If using Apple's transfer process to transfer data to a new device, for Apps the transfer process creates a record of the Apps that are installed on the donor iPad - and it is this record of installed Apps that is transferred to the target (new) device. For those Apps that are still available for download from the App Store and compatible with the target device, the corresponding Apps are automatically downloaded and installed from the App Store.

“Transfer” is rather a misnomer. In reality, your data and setup are merely cloned to the new device. Nothing is moved or removed from the original device:

Transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support

Use Quick Start to transfer data to a new iPhone, iPad or iPod touch – Apple Support

I'm unaware of any native tools by which you can automatically catalogue (i.e. create a list of) the Apps installed on your iPad.

That said, you see a comprehensive listing of installed Apps from iPad settings:

Settings > Apps

While the iPadOS doesn't provide a facility to export the list, you might screenshot the list in sections - and use this to keep record of the Apps installed. If you crop the screenshot(s) prior to saving them, you can use the iPad's capability to automatically extract text by swiping thought the list, copy, and then paste this text into a document.

By example...:

You'll obviously need to repeat the process of extracting the text for each of your sequence of screenshots. In so doing, you can create an alphabetical list of your installed Apps with a minimum of manual effort.

You're very welcome. I am delighted to have been able to offer a working solution.