Ringtone on iphone 5s, 12.3 (purchased in 2019)

That's a strange and apparently difficult one:

I purchased a couple of songs from iTunes and while they do appear in Alarm Clock - Sound - Songs, so that any of them can be set as an alarm ringtone, they never appear in General Settings - Sounds - Sounds and Vibration Patterns - Ringtone - (any of the sections: Ringtone, Text Tone, etc.).

When I select any "Sounds and Vibration Patterns" category, eg. Ringtone, there sometimes (not always!) appears a random line reading "Download all purchased tones" under the "Store" heading, just above the default ringtones (or where the purchased songs appear correctly in the Alarms sounds section). But, as soon as I click on it, after a short "Checking for Downloads" message, the line disappears completely.

I' ve tried signing out and in again to my Appleid account, dowloading again (and again) the songs from iTunes store, and resetting the phone, as advised, but still.

Although not being able to set a particular song as a call ringtone is of course not that serious, I'm curious to find out what the issue could be, so any insight would be appreciated. Thank you.