Anthropic's rate limit are very low sadly, even for paid customers. You can use the API of course but it's not as convenient and may be more expensive.

They seems to be heavily concentrating on API/business use rather than the chat app, and this is where most of their revenue comes from (opposite for OpenAI), but I'm just glad they provide free Sonnet 3.5 chat. I wonder if this is being upgraded to 3.5 new ?

Edit: The web site and iPhone app are both now identifying themselves as "Claude Sonnet 3.5 (New)".

I hit their rate limit one night with about 25 chat interactions in less than 60 minutes. This was during off hours too when competition for resources should have been low.