Whether a tool you make your assets with is compatible with your project's license is irrelevant unless you want to ship your tools with your project. I pose no restrictions on what you do with the fonts you draw and convert using the tool.
The tool itself is not open-source, though my changes to underlying font generator library are published on GitHub, and a list of libraries it uses is available on the help page.
If you want to draw symbols directly on a webpage, BitFontMaker2 is perhaps the closest in terms of workflow. As for my tool, note that you can paste an updated image into it right out of your preferred image editor. I do explain my process and motivation in the blog post.
I may look into allowing to paint in the tool in future, but there is a lot to making an adequate pixelart editor.