My two cents on this. Even if we use VPN and prevent to an extent intermediate routers peaking into packets, then also DNS server queries can still leak. A lot can be gleamed by just looking at the DNS queries even if the packets are encrypted. With other fingerprinting techniques, profiles can be generated with a surprising level of accuracy. Using VPN + Google DNS or VPN + Cloudflare DNS is equal to figuring out what places an individual has been in a day but not knowing what the individual did in those places.
Maybe the best approach is to setup a personal DNS server. it should not be too hard and would not require cutting edge or costly hardware. And use the personal DNS server along with a VPN.
What I mean is, if a Cloudflare customer decide to use some Cloudflare service for their website, in your case, the “human verification security”, it will affect any person connecting to the said site, with Quad9 or anything else.