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Not a brown recluse. Brown recluse have much large bodies, longer legs with different spacing, are fuzzy not shiny, and have a dark "violin" shape on their back.
Also, the venom is only contained in the venom sacks in the head, which in this spider appears intact.
Your cats are probably fine, but consider examining them for bites or taking them to the vet. Also Google brown recluse and see how different it looks from that spider.