In US law, there is no such thing. The shape of a glyph (or many) isn't even slightly copyrightable. This is settled law. Fonts (on computers) have a special status that makes them semi-copyrightable in that some jackass judge from the 1980s called them "computer programs" and so they have the same protection as software... but this won't protect against knockoffs.
I can't tell which way you mean this, but that sounds similar to the situation with most public domain musical compositions - the manuscripts may be completely open but a specific typesetting can still under copyright. And like that case, "just" tracing a font / typesetting a composition is still a fair amount of work.
This person isn't just collecting existing letter shapes; inventing a new letter shapes would be protected by copyright?
There are lots of things that can't be copyrighted.
For example you can't copyright an anatomy drawing: https://www.skeletaldrawing.com/licensing (i.e. the layout of the bones, etc) but you can copyright your specific drawing - but someone else could draw in the same style and not violate your copyright.
Same here: You can't copyright the shape of the letters, but you can copyright you specific ttf program (expression), but someone else can make the same letter shapes if they want.
There are many ways to draw the same letter, as there are many ways to draw a cat.
Also if one draws letters that look like cats, will they fall under copyright protection?
You need something "extra", some kind of style that is distinct.
I'm not saying your drawing has no copyright - it does, if someone reproduces it exactly that's illegal. I'm saying if someone makes the same type of drawing, in the same style, that's not infringement - even if they looked at yours, as long as they drew it themselves.
A font file is more like a config that’s used by your OS to render something, there’s no real interactivity in fonts (except some ligatures but those are just static tables, right?).
I would say that counts as interactivity.
Fonts aren't software in any meaningful sense of the word.
In the United States, it is settled precedent that typefaces are not copyrightable. That doesn't change just because they became digital in 1984.
It is settled law that letter shapes aren't copyrightable. Period.