This is a different conversation from a performance-based termination, and it's worth treating it as genuinely different, not just a softer version of the same script. The person did nothing wrong. They may be losing their job alongside several teammates, on the same morning, for reasons that have nothing to do with them. Say that plainly, don't blur it with language that sounds like it might be about them.
Lead with the fact that this isn't performance-related, in the first sentence, not buried in paragraph three. Don't apologize on behalf of the company in a way that sounds like you're distancing yourself from a decision you were part of delivering. Have HR logistics, severance, benefits, timeline, ready before you start, so you're not fielding practical questions you can't answer. And if you're delivering this to multiple people, keep the wording identical for each conversation, inconsistency between them becomes its own problem.
The people who remain are watching how this is handled as closely as the person who's leaving. Tell the team the same day, factually, without turning it into a eulogy or a pep talk. Don't promise "this is the last of it" unless you know that's true, an unfulfilled promise here costs more trust than saying "I don't know what's next" honestly would have.