Hey!
Congratulations on being invited to the Farrer AC, that is fantastic news!
The group activity in my assessment centre involved being split into teams and you receive a scenario that you will discuss (almost in a debate-like setting). On the firms' website, an example scenario they have outlined is: "Should everyone be able to enjoy protection from media intrusion into their private life, or are there categories of individuals / circumstances where one’s reasonable expectation of privacy must fall away?"
Your team will be assigned either "for" or "against" this question, and you have 20 minutes to prepare your argument (without Google) before debating for 20 minutes with another team. The aim is reach a joint decision!
I did it last year and we had to debate the "green belt". I found this slightly frustrating as people didn't actually know what the green belt was and said things like "we shouldn't build over the Peak District" (which was wrong because the Peak District is protected not as green belt, but because it is a national park), because, as you say, you're supposed to debate without Google (or GPT!). In fact the green belt is specifically a "belt" around sixteen specified urban areas ensuring they cannot grow beyond its borders 80 years ago, resulting in, for example, ruinous housing costs in London.
You have to resist any urge to be informed and opinionated about "best" solutions and instead be laser-focused on ensuring the group is successful in "collaboration" - in particular by keeping time and trying to guide people to a conclusion