The pip-compatible interface of uv is:

uv pip 

and NOT uv run pip!

If you look at uv pip --help, then the -e (--editable) option is listed there.

So, try simply:

uv pip install -e .

and not: uv run pip install -e ..

And simply remove the run inbetween.

I haven't tested it yet - just yesterday in the night read about uv and was fascinated. But reading your question I was like - but why "uv run pip" and not uv pip?