For Android there is an application from Mail.ru "Moosic". There is a function that will copy all the music from VK to moosic ..................................
Previously, there was an application for Apple - VKontakte 2. It allowed saving songs already listened to in the application in the cache. But for obvious reasons, the application has not survived to this day. I don't know any other analogues for Apple.
Another option is Telegram. There is a special bot that searches for VKontakte music by the corresponding request.
You can safely listen to saved from android without VC. Hidden folder .vkontakte in the root of the phone, there is cache audio, you rename everything to mp3 - you enjoy
I heard that soon the music bitrate will be cut to 128 kbps in VK. I think after that many people will switch to other social networks.
Plus no one forbids you to transfer your music library to the same Apple Music or to other programs or sites
You can install Yandex.music and import all the music from VK there, but it is paid 199r (Russian). I recently started using it myself, I really like it. There are also applications that download music from VK, but then you have to transfer it to all devices yourself.
In earlier versions of VKontakte (at least for Android), the entire audio cache was stored in a separate folder ".vkontakte / cache", changing the file extension to .mp3, you could get ready-made audio recordings. When VKontakte closed access to audio recordings through the VK API methods, apparently at the same moment the files from this magic folder disappeared (even with the display of hidden files turned on).
You may be able to find something if you connect the device to a PC, but this is not accurate. And I don't know any applications that can recognize the cache of other applications.