Trying to avoid using SD Cards.
Can the Home Assistant Pi image be installed and run from an external SSD attached to a Pi4?
Yes, and there are sooo many guides available. Just search for it, and find one that suits you best.
Only tip of advise: make sure you get a sata to usb converter that is supported. Google that list too to have the latest and most up to date list to ensure full compatibility.
This is what I followed, worked fine for me: https://youtu.be/Ks-GxF6sd5M
Since HASSOS is at 5.11 now, is downloading the beta still required? Do you know if 5.11 has the capability of running an external SSD?