before running pvresize, you’ll have to move the partition’s end to the end of the disk. Not for the faint of heart, but easy: Using fdisk, delete your old (too small) partition and re-create it, letting it use all disk space. Reboot using recovery system, run pvresize, reboot.
fdisk will only change the partition table only - therefore the partition’s contents will remain.
pvresize will run on a live PV, AFAIK - but to avoid unnecessary risks, an isolated recovery system boot would be my choice.
And again: If you need that data on that machine - back it up (first). But that holds true even if you’re not running any of these changes…