skills="all" does not add "Skill" to tools

[RunOrVeith]

Claude can sometimes not use skills with skills="all" and defined tools

All examples in the documentation set skills="all" and that's it, seems to work.
I have spend a whole lot of time debugging why my skills suddenly don't work anymore:
Apparently, you still need to add "Skill" to tools if you define tools explicitly.
This only happened while running my agent in a kubernetes job, locally everything worked fine. I have no idea why, probably something in my global settings that gets read locally but is not available in the cloud.

ClaudeAgentOptions(
            # ... other stuff
            setting_sources=["project"],
            tools=["WebSearch", "WebFetch", "Read"],  # <-- I had to add "Skill" here for it to work
            allowed_tools=["WebSearch", "WebFetch", "Read"],
            skills="all",
        )

This is especially confusing since the doc string of allowed_tools reads to "configure everything", which does not seem to be the case.