How broken is the screen? Does part of it work? Does the touch function work?
I ask because to transfer over USB you will need to be able to unlock the screen. If you can do that with a fingerprint, great, but if not then you'll need to enter a PIN, and that will be easier if either touch or display works: if display works and touch doesn't you can connect a keyboard or mouse to the USB port, if touch works and display doesn't you may be able to mirror via an HDMI adapter to an external display (I'm assuming the S9 would support this here). If neither works then unlocking is fun: I've done it blind before now, using a keyboard (cursor keys to navigate, enter key to select), but I practiced using a working phone before trying it with the broken display.
Then it's a question of what you want to transfer: different types of data may require different methods. Images you can just copy over USB to a computer, stuff like SMS you'll need to run a backup app and then copy the backup off the phone. Basically data that are "internal" to an app live in databases in areas you can't see from a computer with a USB connection. And of course some stuff will probably have a cloud backup. So it really depends on what you are trying to recover.
As for erasing it, it would be easy if the bootloader were unlocked, but that sounds like a long shot. If you can get mirroring and controlling going at the same time (e.g. HDMI mirroring plus a bluetooth mouse or keyboard to control it) then it would be easy, but the pairing a bluetooth device with the screen broken takes a lot of patience (I've done it once, and these days I have a multi-device BT mouse which is already paired to my phone, just in case I ever need to do something like that again...).