I have two VPNs. One for privacy (e.g. general browsing) and one to reach my home NAS (e.g. to reach my selfhosted image backups). Is there a way to set the system up so that when I use applications X, Y and Z, it should use the privacy one, and if I use A, B or C, it should use the private one?
You might consider a more elegant approach to accomplish your goals.
For example, I run Tailscale on all of my devices. They are accessible to each other (at all times) through the encrypted “Tailnet” while each has its own public internet provider (my home ISP, my cellular provider, my VPS host, etc).
They all route their DNS requests through my home server which is running Adguard (for DNS ad blocking on every device). If I wanted I could route all their traffic (not just DNS) through the home server, and I could have the home server’s internet-facing interface connect through a commercial VPN to then hide all that egress traffic, across all my devices.