If you are using partitions then you have to reboot to use new space. I didn't find a way to avoid this. If someone has let me know.
However, reboot should be done after you extend last partition on the disk or add new partition. Doesn't make sense to reboot before.
First thing you should notice after rescan is bigger disk size in fdisk and in lsblk. If you don't see it you have to play with these echo 1 and echo --- commands.
After you see more space you can extend/add partition, then reboot, extend vg, extend lv and fs.
If you want to avoid reboot you have to assign raw sda/b/c disk to volume group without partitioning it to sda1/2/3. Then there is no need for reboot.
Partitioning was necessary some time ago when linux could not boot from LVM, but now it can.
If you do lsblk you will see partitions or lvms depending on if you are using partitions or lvm, you can have all parts if you don't use lvm or all lvms if you don't use partitions. Here is one example:
root@srv4 ~ $ lsblk
NAME MAJ:MIN RM SIZE RO TYPE MOUNTPOINT
sda 8:0 0 7.3T 0 disk
├─sda1 8:1 0 500M 0 part /boot
└─sda2 8:2 0 7.3T 0 part
├─vg_srv4-LogVol13 (dm-0) 253:0 0 7.1T 0 lvm /
├─vg_srv4-LogVol05 (dm-1) 253:1 0 100G 0 lvm /var/log
├─vg_srv4-LogVol04 (dm-2) 253:2 0 20G 0 lvm /var
├─vg_srv4-LogVol01 (dm-5) 253:5 0 20G 0 lvm /opt
├─vg_srv4-LogVol00 (dm-6) 253:6 0 20G 0 lvm /home
├─vg_srv4-LogVol03 (dm-7) 253:7 0 20G 0 lvm /usr
└─vg_srv4-LogVol02 (dm-8) 253:8 0 8G 0 lvm /tmp