feat: add claude_code_web in claude-code

[BrunoQuaresma]

No description provided.

[bpmct]

We want to make this configurable in the module. See #129 so we can mark this as a draft once I get it working and perhaps @DevelopmentCats could help take it to the finish line unless you want to add the TF logic

[hugodutka]

Converted to draft - this needs more work before it's ready to merge.

[code-asher]

Uh sorry I accidentally pushed to this branch (I am basing the agent status work on this since I need agentapi). I removed the commit.

But also, I think that means the api cannot become optional if we need it for the status reporting?