Strange result with knife project in 3.0

I’m trying to use knife project to cut an oval hole in a grid. I select the grid, go to edit mode, select the oval (from the outliner), go to top view, and then knife project.

It works sometimes, but most of the time it doesn’t work at all or I end up with something strange, like this:

What’s going wrong here?

These are the steps that I follow. The only difference is that I select my curve from the outliner, but I have tried to select it with ctrl + left-click too, with the same result.

The knife tool should cut exactly along the projected curve but in my case the cut seem to follow the mesh grid somehow. Sometimes it follows the grid squares exactly and I end up with a cut that looks jagged or pixelated.

Is there some known situation where the knife tool behaves like this? Are there any restrictions to what objects it can cut?

Further exploring it seems like I get bad results when zoomed out, but not when zoomed in(?!)