A year ago, I was getting into NYT crosswords myself and had the idea to make one too. I wrote a tool in Elm to help create do the task.
It helps with drawing the grid and retaining rotational symmetry. It indicates clue numbers in the grid, as per NYT placement. It allows hovering over a square and typing a letter to begin filling.
I intended to add a way to indicate a problem with the grid to help notice things like erroneous 2 letter answers or non-contiguous empty space, but I never did get around to it.
In case you’re interested, it’s here: https://crossword.wfl.space