One million hits in 24 hours is only 11 TPS, if that's causing issues, then Anthropic isn't the problem, your application or hosting is.
https://fosstodon.org/@readthedocs/112877477202118215
A bunch of the traffic hit the origin.
I think they'll survive this massive DDOS of 76MBPS.
Same in the case of ReadTheDocs which was linked above, 10TB of traffic over 6 days, an incredible 19.29MBPS sustained. Has humanity even built technology powerful enough to handle this massive assault?!