The future? This is already happening. The /chatGPT subreddit is full of people talking about how they are using it to "talk with" their dead relatives. They show chatgpt a lot of the writing of the relative and then the AI pretends to be that person.
This will, of course, only get more and more. I've never seen that Black Mirror episode, but I've been saying that for years: in the future no one will "die" anymore. As soon as they die for real, an AI will take take their place. Imagine a room of your home with AI versions of your entire ancestry, available to talk whenever you wish. It won't even require scanning things in for people who are already alive, as some currently do with chatgpt and as you describe in that episode, as most living people have already interacted enough with AI for AI to be able to mimic them to some degree.
Is this a bad thing? I don't know. The actually person will be long gone. It's not like we are capturing their consciousness in the machine. So would this kind of computer mimicry be that different that staring at photos of them? Most people never really know anyone further back than their grandparents. Even their grandparents they often only know as happy old people who always gave us candy when we visited. AI might provide the chance for people to actually meet and get to know their family in a way that's impossible right now.