Steam mobile doesn't allow you to use adb backups to move steam guard keys to your new device. This means if you use WinAuth or other tools that use the steam guard private key obtained from a rooted device, they will stop working when you switch devices and set up a new steam guard. The process below will allow you to move your steam guard key from a rooted device to an unrooted device.
notes:
A. when installing old versions of apps from unofficial sources, it's important to verify that they're legitimate. One way to do this is to install the old version, then try updating it through the play store--this process will not work if the signatures don't match.
B. don't keep unencrypted backups around. 2fa doesn't help if someone else gets ahold of it. Titanium backups are standard compressed files/folders, and adb backups are tar files with a few extra bytes at the beginning (the beginning of the file is at a fixed offset), and it's trivial to extract files from them. I'm not sure how secure adb password protected backups are.
C. adb backup comes with a warning that it may be deprecated. if it is, the adb shell command may help, I believe there's a backup command in the shell somewhere (ab
? not sure). On the other hand, that may also be removed at the same time.
In my case it was possible to make a backup with this command - "adb backup -f valve.ab -noapk com.valvesoftware.android.steam.community", then "adb restore valve.ab". Tested on steam 2.1.4 and S20+ unrooted.