README says to run:
uv add "mcp[cli]"

If anyone will follow this advice she'll get the error:

error: Requirement name mcp matches project name mcp, but self-dependencies are not permitted without the --dev or --optional flags. If your project name (mcp) is shadowing that of a third-party dependency, consider renaming the project.

The instruction is completely wrong.
One needs to first create its own project. Initialize it with uv init and only then can use the uv add command. But even then the subsequent calls of mcp won't work because uv add does not install mcp[cli] as a command. The best way to run mcp cli via uv is uv run mcp.

In general the README.md in current state can be a source of confusion.
Someone has already reported this #111 but it was not addressed.