>>chamom+(OP)
Looking into this more, it does indeed seem to be a cloudflare problem. It looks like cloudflare made a significant error in their bot fingerprinting, and Perplexity wasn't actually bypassing robots.txt.
To be honest I find cloudflare a much more scammy company than Perplexity. I had a DDoS attack a few years ago which originated from their network, and they had zero interest in it.