lcalamar u can use your own dns when using a vpn. I've used my own dns while using a vpn. Pihole & unbound which forward your dns queries directly to root dns servers.
When i did a dns leak test with this setup, my dns ip was allways my home ip. Recently i came aware that websites also have the possibility to track what dns u use.
So in that case my ip was hidden for websites, but if it tracked what dns server i used, it would see my home ip as dns, which is very identifiable as i'm the only one using it. I've decided recently to keep that setup (pihole + unbound), but route that traffic through another vpn tunnel.
Your concers about vpn's are inherently true for dns aswell. Either you trust your ISP, or whoever else is hosting the dns server.
As of now, there is no real 100% privacy friendly method of dns available, as far as i know.
The closest thing, in my opinion, would probably be your own dns with upbound, so skipping all dns-servers in between and directly asking the root dns-servers, and then tunnel that dns traffic through tor.