You need a hardware like a raspberry pi 3 or 4 then you install a distro server like yunohost, which also gives you many other services like email, chat, cloud storage and many more. Then you install nextcloud and inside nextcloud there's next cloud music, you install it, move your music there and use a client like subsonic on your phone. Done
Discussion
Thank you for the quick explanation!
But new music exploring might be a problem within the own library. But therefore I could explore songs still on YouTube for example. But could be still nice!
A thing that’s more important to me right now is, that I create my own media cloud so I can have my pictures and videos at home. Searching for a good NAS :)
IMO the best option is yunohost with nextcloud and prism: