You will need to load the drivers into the kernel, and also ensure you have the mod file needed in grub.
I have never tried to combine different types of block devices into the one volume group, and I would strongly recommend you do not mix types of drives in the one VG.
In your case it is also more difficult, because iscsi, is a layer 3 protocol block device. I am not sure you would be able to get the iscsi initiator to connect to the drive, and then lvm to bring up the VG. I may be wrong, but I dont think it can be done easily, and would not be stable even if it was done.
I would suggest that you use a live cd as you have done, boot and mount the current VG. Ideally move some files to a usb drive, or network store temporally. Then resize the logical volume and the VG back to how it was.
Create a new pv/vg and logical volume for the iscsi drive, and then create the partitions you require and mount those partitions in non-boot required directories, eg /home or if it is a web server maybe /var/www. This will allow for the server to boot with only the main drive, and then during the boot processes, assuming iscsi config is saved, it will mount the non critical drive.
The main directories the server needs to be boot are:
/etc, /usr/sbin, /usr/bin, /var/, /usr/, /lib/
The /usr/sbin and /usr/bin gets mounted via symbolic link to /sbin and /bin
If you /boot is not on its own partition, then that would also need to be on the main lvm.
Also ensure you fstab, has the partitions on the iscsi drive listed, once you have moved the data over.
Once you have booted off the live CD mount the volume group as you have it currently. to /mnt/newroot
Then run:
mount -R /run /mnt/newroot/run
mount -R /dev /mnt/newroot/dev
mount -R /proc /mnt/newroot/proc
mount -R /sys /mnt/newroot/sys
chroot /mnt/newroot
This will change the root be the root of the Volume group, you will then be able to access all your directories etc as if you have just booted into that os.
run mount -a
This will mount all the mount points that are in the brokensetup.
you will need to add the options in the kernel line of grub similar to, the easiest way is to add the line, into /etc/default/grub as the GRUB_CMDLINE_LINUX_DEFAULT for example:
GRUB_CMDLINE_LINUX_DEFAULT="ISCSI_INITIATOR=iqn.2024-06.au.com:client ISCSI_TARGET_NAME=iqn.2024-06.au.com:server ISCSI_TARGET_IP=10.0.0.250 ISCSI_TARGET_PORT=3260 root=UUID=6c816f51-0613-45e7-a15b-bc2d5cd00f88 ip=10.0.0.100::10.0.0.1:255.255.255.0:client:eth0:off "
ISCSI server in this example is 10.0.0.250
ISCSI client is 10.0.0.100
Gateway 10.0.0.1
Subnet 255.255.255.0
You will need to change these to match your case or use DHCP
The ip variable sets a static IP for the machine, if you want to use dhcp, you need to have ip=dhcp the root=UID=
Once you do all these changes, you will need to run update-grub, and cross your fingers.
This should initiate iscsi before trying to running the lvm provision script, and hopefully, it will allow you to work as normal.
**note this is theory only, as stated earlier, I have never tried to have a vg, with a iscsi drive, and a internal SATA/SAS drive.