It's tricky to do for large public websites, because routing happens at the IP level while users want to input a domain name.
That domain could constantly resolve to different IPs, requiring updates to the routing rules, and those IPs could be shared with many other domain names that the user didn't list (for example Cloudflare IPs). So the mapping isn't clean and you're likely to miss some IPs some of the time or incorrectly intercept some traffic that the user didn't want to route through the VPN.
A proxy would not have this problem, it gets to inspect the request and hostname and then decide how to reach that host.
VPN app can still solve it by locally resolving configured domain into special local IP, which get VPNed into real IP on their side. You'll need to encode original DNS name into protocol somehow, so that remote side knows which real IP to access, but it is certainly doable.
That domain could constantly resolve to different IPs, requiring updates to the routing rules, and those IPs could be shared with many other domain names that the user didn't list (for example Cloudflare IPs). So the mapping isn't clean and you're likely to miss some IPs some of the time or incorrectly intercept some traffic that the user didn't want to route through the VPN.
A proxy would not have this problem, it gets to inspect the request and hostname and then decide how to reach that host.