Maybe I am not correct but as far as I can see there are two sets of sounds here … and the reason for my post is that I beleive the text of your request just deals with the second set.
The first set is stored in the bell device and the chime unit - these sound when the bell is pressed … and the second set are the ones in the app itself which sound through the device the app is running on. As far as I can see the ones in the bell sound regardless of it being connected so if the device is off line they still sound. The chime needs to be online but they are a defined set of tones available to choose from in the chime unit.
I already use my alexa to make announcements based on the bell push - eg alexa announces “there is someone at the door” when the bell is pushed … but the person standing on the doorstep just hears the one I selected from the limited choice of tones in the bell itself … and the app running on my phone plays the tones I selected there which could be different from the doorbell.
I previosly had an MP3 doorbell where I could upload a sound file and it would use that so I could change the tune depending on the season and how I felt … I could use “happy birthday” on the days of peoples birthdays, a christmas tune at christmas etc …
So … my request is specifically about being able to load tunes to the bell and chime devices and not related to the tunes the app plays - from reading your request it did not seem to cover this first set of tunes.