From what I understand they have... or will have... 2 data centers, the original one ("Colossus 1", the one that is already poisoning Memphis, TN) is the one Anthropic will be using, but they are also building a new one, Colossus 2 for Grok's own use.
All that said, I wasn't aware Grok really had any ground to lose, the only time I ever heard about it is twitter memes and when its getting in trouble for claiming itself "Mecha Hitler" or serving sexualized content.
> Downloads of Grok fell to about 8.3 million in April, from a high of more than 20 million in January, according to analysis firm AppMagic.
They have a ton of spare capacity, hence they are letting anthropic use it.