Even if your new router would allow for it:
Shifting DHCP (which -as mentioned- is strictly an IPv4 protocol) from that router to Pi-hole may not address your issue. The router may still advertise its own IPv6 address as local DNS resolver.
You should search for IPv6 DNS management options for your existing router first.
If they are available and support the configurations suggested above, then you would be able to avoid the IPv6 by-pass of your Pi-hole.
If that doesn't work out, you should also scrutinise your aspired future router for its IPv6 DNS configuration support. From the reports we see, quite a few models would lack that support, leaving you no better off than now.