Whoever thought that 100 GB for pve/root would ever be enough, or not asking how large pve/root should be during the install, or not allowing for backups to be stored in local-lvm needs to be sent back to school.

Any of the above three solutions would make this entry obsolete for the most part. Alas that is not the reality that we suffer.

resizing pve/root is something best done when pve/data is completely empty. so I try and do this during the initial setup of a new ProxMox host.

Just follow the below steps and adjust the lvresize and lvcreate for the sizes you need. In the below example I am adjusting a 4TB Raid 10 to allow for 1TB for pve/root and the rest to pve/data.

lvremove /dev/pve/data -y
lvresize -L +900G /dev/pve/root
resize2fs /dev/pve/root
lvcreate -L 2.65T -n data pve
lvconvert --type thin-pool pve/data