I tried also to install HassOS in RPi4 and SSD but get lots of problems. I have now Hass installed on Debian Buster Lite. Boot from SDCard and rest from SSD (root).
Work perfect here, and use the old root part of de SDcard as a fallback part.
Sometimes rsync ssd root to sdcard root. When Hass is crashing you can update the cmdline.txt back to SDcard root and boot up, rsync back and your SSD is running again.
Here steps maybe it will help you also:
Flash on SD Card Debain Buster Lite Image (Use Etcher) Here on OSX.
on PC or OSX go those steps:
sudo touch ssh
sudo nano /boot/wpa_supplicant.conf
Add line:
ctrl_interface=DIR=/var/run/wpa_supplicant GROUP=netdev
update_config=1
country=NL
network={
ssid=“YOUR SSID”
psk=“YOUR PASSWORD“
}
Format SSD with FAT and then put SDcard in RPi4 and connect SSD also.
After SDcard is booted do these steps:
sudo mkfs.ext4 /dev/sda1 -L root
sudo mkdir /media/newdrive
sudo mount /dev/sda1 /media/newdrive
sudo rsync -avx --progress / /media/newdrive
sudo nano /boot/cmdline.txt*
Copy the full line in the cmdline.txt and comment out 1 with # in front
Replace the second line the “root=“ see below.
If you have something with resize, remove that part also.
root=/dev_/sda1 rootfs_type=ext4 root_wait rootdelay=5
reboot now*
Correct location and timezone
raspi-config
Make IP Static / Only when its needed 
sudo nano /etc/dhcpcd.conf
interface wlan0
static ip_address=192.168.100.24
static routers=192.168.100.1
static domain_name_servers=192.168.100.1
Install Docker
sudo -i
apt-get install software-properties-common -y
apt-get update
apt-get install apparmor-utils apt-transport-https avahi-daemon ca-certificates curl dbus jq socat
curl -fsSL get.docker.com | sh
Install Hass.io
curl -sL "https://raw.githubusercontent.com/home-assistant/hassio-installer/master/hassio_install.sh" | bash -s -- -m raspberrypi3
After about 20 Min login via WebUI. Create account
Copy backup files to the backup folder on new install
reboot now
Restore latest backup
/usr/share/hassio/backup
After restore is done shutdown HA only
Remove home-assistant_v2.db
reboot now