Install to the M.2: other images
The image is written to the M.2 as a fresh install, so you set it up again there. First install the drive and run m2_init, and put the image's .img file somewhere the running system can read it.
Install the image onto the drive
cd ~/ps5-linux-tools
chmod +x ./m2_install.sh
sudo ./m2_install.sh --install /path/to/ps5-ubuntu2604.img
Start from the drive
cd ~/ps5-linux-tools
chmod +x ./m2_exec.sh
sudo ./m2_exec.sh
To start from the M.2 every time, edit /boot/efi/cmdline.txt and change root=LABEL=ubuntu2604 to root=LABEL=ubuntu2604-m2, see Boot options.
Switching distros
There is no need to format the drive from the PS5 OS again. The PS5's format only rewrites the blocks it uses itself and leaves the Linux partition as it is. To change distro, format the Linux partition from Linux (sudo mkfs.ext4 /dev/nvme0n1p1, the partition m2_init created) and install the new image.
No 64 GB USB drive?
A USB drive too small for the full image can still get you onto the M.2: the community script at github.com/g4caos/ps5-linux-script copies the running Linux system to the M.2 drive with rsync, so no image file is needed on the USB side.