root access - How to install SuperSU using adb while the phone is in TWRP recovery with a broken screen

I have a Samsung Galaxy S4 SHV-E330S with a broken screen (cannot see or touch anything). Please see this and it's comments for more context

I have managed to flash TWRP on this phone (https://twrp.me/samsung/samsunggalaxys4ltea.html) and now I can boot the phone into recovery mode and during this time I can use adb to get a root shell on the phone

I would like to find a way to stream it's screen to the laptop monitor and control it using adb, but I suppose I will need to root the android OS first to this more easily

I cannot use the phone screen so I am not sure how I can install SuperSu.apk from the phone itself. Is there a way to install it through adb? I think the adb shell I get while the phone is in recovery is not the android OS if I understand it correctly, so I don't know adb pm install while in recovery will install the apk correctly. Using adb to control the phone while in recovery is the only I can do anything at all with this phone at the moment so as far as possible I don't want to do anything wrong which might make me loose control of adb during recovery. What is the best way to go about this?

Or is there any way to get adb authorization for android OS, without root and completely through adb while in recovery?