You can connect your cyberdeck to the broken tablet to retrieve information that includes a key for the door.
Edit: I thought I wrote a walkthrough and I’m flipping through the concise user’s guide and I completely skipped the walkthrough for this game lol.
So I had to look in the code, and there were several places I put in an action for examining the tablet. But only one is connected.
Full disclosure: I was not sleeping while writing this. hahaha.
Regardless, to answer your question: go back to the room you found the tablet in, and you’ll have an option to try to hack it. That was meant to be a Use action in the inventory. Apologies.