I don't understand how Files app integration with cloud storages
works.
The first thing to know is that iPadOS does not store files like Windows, Linux or macOS does on computers.
On computers, you can directly create folders and save and organise your files in whatever folder anywhere on your disk. (Apps on computers will thus ask you where you want to save a file). But on iPadOS, a user doesn't create folders to organise their files in it. The iPadOS does this automatically for you.
When you install a particular app from the App Store, like Pages or MS Word, iPadOS automatically creates a folder (or more than one, if necessary) for each app. The app then usually save any files created by it in these specific folder(s). Other apps aren't allowed to directly access them - only you can manually open file from another app's Folder.
This allows iPadOS to automatically organise the files in your device and also keeps it secure.
This is why when you open the Files app and select 'On My Device' (under 'Locations'), you will see that all the folders shown in it are named after the apps you have installed on your device.
(Note: Latest versions of the Files app now allows you to create your own folders too).
The Files app also integrates with online storage services, like iCloud Drive and Yandex.Disk, and these can be accessed under 'Locations'. Tapping any of these locations will show you all the files that you have uploaded to these services.
I also have Yandex.Disk visible ... and I can download files from
there. The issue is that I have no idea how to delete files which were cached in Files app.
Apparently, the Files app has a different approach of working with cloud based storage.
If you tap to open any file from any cloud storage services, the Files app tries to simulate the experience of opening a file from them similar to you opening a file from your device.
Since this cached file acts like a direct link to your file on the cloud storage service, iPadOS doesn't allow you to delete it manually. (With iCloud, any changes you make to these files - like a Pages or Word Document - will also be saved directly to the file on iCloud).
So opening a file directly from a cloud based service in Files app is not equivalent to downloading it permanently for offline use.
This is the confusion you are experiencing with the Files app - you think you are downloading a copy of the file from the cloud storage, where as iPadOS treats it like a link to the file on the cloud storage.
To actually download a copy of the file from iCloud or Yandex.Disk to your device that you have full control over, you have to copy the file to a folder in your device in the Files app. (See - Use the Files app on your iPhone, iPad, or iPod touch - to know how to do this).
As for the cached files, they are automatically deleted by iPadOS when you are running out of disk space. The cached files can also be deleted by signing-out of the cloud storage service. (More details here - Can’t delete ‘locally stored’ content in the Files app? Here’s what’s going on).
Yandex.Disk mounted as "Read-only"
As @Shock9616 explained in another answer, Yandex.Disk may be "Read-only" by design on the Files app as Yandex would like you to use their own dedicated app Yandex.Disk. So it would be better to use Yandex's app when you are downloading or uploading files from Yandex.Disk.
