I deleted a partition that was a physical volume part of a volume group. I also tried at the same time to expand a logical volume.

I try to restore but get errors:

[root@server ~]# pvcreate --restorefile /etc/lvm/archive/vg_nas_00037-357471831.vg --uuid UMWCdg-NYnK-5e3B-b4uT-M4ze-AUXH-cva41T /dev/sdc1
Couldn't find device with uuid byRq7r-cGBg-v1Vc-fXbm-GrFt-VzLW-oVjIo9.
Couldn't find device with uuid UMWCdg-NYnK-5e3B-b4uT-M4ze-AUXH-cva41T.
Physical extents end beyond end of device /dev/sdc1.
Format-specific initialisation of physical volume /dev/sdc1 failed.
Failed to setup physical volume "/dev/sdc1"

That first "Couldn't find device ..." is normal, and expected if the old LVM header on that partition has been overwritten. That "Physical extents end beyond end of device /dev/sdc1" sounds like you re-created that partition with a size smaller than it was previously. In that saved configuration file, look at the "dev_size = ..." line for that partition. Your partition must have at least that number of 512-byte sectors.

The new partition might be getting megabyte aligned wher it gadn't previously - would explain a small change maybe.

... and of course if you expect to recover the filesystem(s) previously in that PV, you must have the starting location exactly where it was before. If the PV header is still there, you can use hexedit to look for the ASCII string "LABELONE" at the start of a sector, and that would be the 2nd sector of its partition.

And, there are two PVUUID missing, when you restoring only one.