FontForge is a free and open source font editor with bitmap font support and a pretty nice bitmap editor, and it can output .fnt/.fon and BDF bitmap fonts, as well as vector fonts with embedded bitmaps.
https://fontforge.github.io/en-US/
In my own game, I use TTFs with dummy (empty) vector glyphs and embedded bitmaps, and the rendering framework I use renders the bitmaps just fine.
Unfortunately it has no way to transform images into bitmap fonts, but there might be something that transforms images into BDFs, which you can then open with FontForge. I mention BDFs specifically because that’s the easiest format to generate automatically, since it’s very simple and human-readable. If there isn’t such a tool, one could probably write one fairly quickly. Though, with a small font like this, it would probably be pretty quick to just redraw the characters in FontForge.