The pro plan does include Opus usage. I've noticed the limits on the web client are a bit higher than through CC, but probably more because of the increased token usage of agentic coding in general.

Claude web is actually pretty good for dealing with random projects outside of code. I have a Home Assistant MCP server [1] behind a Cloudflare tunnel exposed to it that makes maintaining automations a lot easier.

[1] https://github.com/homeassistant-ai/ha-mcp