"How do I ensure that when a disk is Hot Added to one of my Veeam Proxy servers, that disk uses a certain storage policy?"
The snapshot is taken on the original VM and snapshots inherit Storage Policy from parent disk so this is the SP that will be applied to these new (snapshot) disk Objects.
"Lately I've been having latency issues during Veeam replication jobs, and (among myriad other things) I noticed that my veeam proxy VMs are all set to FTT=1."
Do the necessary checks that may help e.g. there are not a chain of unconsolidated snapshots that you/vmsd/vSphere are unaware of, ensure your backup+vCenter+ESXi are on best-suited and compatible builds, ensure you not using quiesced/vmem snapshots where not required, talk to your backup vendor about possible optimisations/issues.
"I want to set all the hot added disks to FTT=0 (why do twice the amount of work when these disks are transient?) when they are added."
Just so you are aware of why the snapshots are there in the first place: this is generally so that VM data can still be written while the proxy reads the data off the parent disk - if you are fine with all the data being committed during backups being FTT=0 then sure but this doesn't make much sense, storing anything persistant or valued as FTT=0 doesn't seem wise in my opinion.
"I have a policy called FTT=0."
I have one called that too, it has rules set to FTM=RAID5/6,FTT=2,SW=12,OSR=100 and confuses anyone that tries to use it in a 3-node Hybrid cluster