Either was already enabled or utilized a custom recovery and modified build.prop.

Perhaps the prompt wasn't on the broken part? Can also plug in a keyboard and use that if you know the sequence.

Not OP. I faced a similar problem once.

I found a friend that owned the same model of phone as mine. I used his phone to approximately eye-measure where on the screen I have to press after entering the Settings app.

Now I repeated these presses on my phone. Luckily, although my phone was broken and the screen had become almost fully black, the touches registered.

----------- edit:- If you find it difficult to find a friend that owns your unique phone, your local mobile shop might have a demo phone for you to try out.

Or Youtube search for a video titled "How to enable debugging permissions on Samsung S8?"

The comment said 'mostly broke', many people are familiar enough with their phones and the various screens prompts to do this without looking at all, or with a little guess work with help from various only resources, images & videos.

in my case a simple USBC-2-USB adaptor allowed me to connect a mouse and it worked right away

like this: https://www.youtube.com/watch?v=2wggP-e3A1Y

stupid as it looks it saved my data without any sophisticated repair

I actually have the perfect(?) solution to this ridiculous problem after it happened to me a couple of months ago.

Hit the Google Assistant button, ask it to turn on "TalkBack". Now you can browse the interface the same way someone blind would browse the interface. Plug in a USB keyboard.

From here you go to the Settings page and enable Developer Tools.