you have but thought of programming an Alexa skill for nextcloud to read appointments or music from a folder nextcloud (such as Hidrive Skill also and German Cloud)
For the calendar, you could try any app or skill that is based on CardDAV.
If a music player supports files from webdav, you can use that.
I wonder which advantage it should bring to use Nextcloud as a “save habor” for your data and then give Alexa and Co. access to it - privacy couldn’t be the main driver in this case?!