lvm restoration in initramfs

Formatting a PV with pvcreate affects only the 1-megabyte PV header. It does not touch the rest of the partition. All that is needed is to reformat with the correct UUID and restorefile. That will allow vgcfgrestore to restore the VG configuration, making the LV(s) and content available again.

Good to know. However since the OP doesn't seem to have any actual backups perhaps they should backup the whole partition first to an external drive with dd such as
dd if=/dev/sda4 conv=sync,noerror bs=64K | gzip -c > /usb/drive/file

Then if something were to go wrong with the vgcfgrestore operation they could restore the partition from the usb drive backup to its previous state and try again. Without a backup if something went wrong their only copy of the data would be corrupted.

It's always good to have a backup when doing recovery work, but vgcfgrestore also affects only the 1-megabyte LVM header.

It's always good to have a backup when doing recovery work, but vgcfgrestore also affects only the 1-megabyte LVM header.

It sounds like if an expert uses all of the right commands only two 1 MiB headers will be affected and not the actual extents. However if someone, not an expert, used the wrong command such as vgcreate instead of vgcfgrestore then the data extents would be affected and possibly reformatted. This is what I meant by something going wrong. If all of the correct commands are used you wouldn't need the backup. I perhaps shouldn't have used the correct command vgcfgrestore in my previous comment and simply stated if something were to go wrong with the attempted restore operation.

vgcreate, like all of the other LVM commands, affects only the LVM header. As long as you don't try to write to any of the LVs, your data will be untouched. All of the information about the entire volume group is contained in that header. There is no LVM information elsewhere in the physical volume. The only danger is if you have a mistake in the partition table such that the partition starts in the wrong place. That will result in an LVM header being written where it shouldn't be.

[EDIT] OK, there are LVM commands like "pvmove" and "lvresize --resizefs" that do affect the data area of the LV. Those aren't the sort of commands you are likely to be running in this situation.[/EDIT]