I have (somewhat) rebuilt my Proxmox cluster and learned a couple things while doing so: an approach to migrating VMs/containers to a new cluster and renaming storage pools.
An Approach to Migrating VMs/Containers to a New Cluster
To migrate the VMs/containers I wanted to keep, I took a backup and stored them in an NFS export. On a node in the new cluster, I restored them from the same NFS export.
I have not looked into it yet, but I suspect that Proxmox Backup Server may be the more appropriate solution for this task.
Renaming Storage Pools
While setting up and migrating things to the new cluster, I was mysteriously running out of space (already). It turns out that my data storage pool was configured with the wrong LVM LV (pve/data) when it should have been data/data (data thin-provisioned LV in the data VG).
I deleted the data storage pool and recreated it as pve-data. Then I created a new storage pool with the correct VG and LV.
Next, I went through each VM/container and updated its configuration such that the disk(s) are said to reside in the pve-data storage pool. The configuration can be found in /etc/pve/nodes/$NAME_OF_NODE/qemu-server/$ID.conf for VMs and /etc/pve/nodes/$NAME_OF_NODE/lxc/$ID.conf for containers.
Source: https://forum.proxmox.com/threads/change-the-name-of-an-lvm-storage.157676/
Finally I went to each VM/container and executed Move Storage for each disk, moving them from pve-data to data (data/data). Once that was all done, the pve-data storage pool was removed.