Firefox bypassing Pi-Hole even after setting Firefox network.trr.mode to "5"

No. This is already handled with Pi-hole, but it is only effective if the DoH setting in Firefox is enabled by default. If you have toggled it off and then back on, the canary domain will have no effect, since you have made a deliberate decision to use DoH.

https://github.com/pi-hole/pi-hole/pull/3166

After you have eliminated DoH as a problem, ensure the host OS running on that client is using Pi-hole (and only Pi-hole for DNS):