The API has a very clear ToS prohibiting third-party client usage with the heavily subsidized Claude.ai subscription plans. Anthropic's right to reject or block that traffic, as well as to ban users who attempt this, is well-protected by the ToS those users neglected to read.

Regarding the legal demands here, anyone can issue anyone else a cease and desist order at any time, for anything, in the USA. The demands do not need to have merit.

"Illegal" generally refers to criminal law, not civil suits, this was essentially Anthropic threatening to file a lawsuit. Opencode was under no legal obligation to comply and was not breaking any laws, they simply decided it was easier and cheaper to comply than to fight.