It's kind of cheating, but Braille should all fit in a 3x2 font.

You'd need a language that doesn't rely on accent marks or pictograms for sure (unless they have a very tiny set of characters), and that probably eliminates a lot of languages.

Latin accents could perhaps be represented as digraphs for such a tiny font.

Some languages have an official mapping, like in German where you can usually replace ä with ae, ü with ue, and so on.

Otherwise the accent could be a separate character, as in cafe’. Probably would be acceptable for this application.

Scripts are products of their processes. For example, musical notation looks the way it does because it was created when people used quill and ink to create the notation. Scripts that we use for writing have their origins in hand-writing and printed wood/lead.

So it's also possible to flip this around. What script could be designed with its basis being a 3x3 grid? That would allow you to create forms which are maximally distinct from each other, without needing to conform to a script like Latin characters.

Has been done, Marain script from Iain M. Banks' Culture novel series:

https://www.omniglot.com/conscripts/marain.htm

All may not get so close to seeing the light outside the Biau of Sin ai: https://news.ycombinator.com/item?id=38800719

If you think about that, 2x3 or 3x2 is the practical minimum. A fully empty glyph and a single dot wouldn't be really useful, and any translation would be too ambiguous for 2x2 grid, so we only have 8 possibilities:

    .@  .@  @.  @.  @@  @@  @@  @@
    @.  @@  .@  @.  ..  .@  @.  @@

This is too small for any actual, natural written language. 2x3 and 3x2 significantly increase possibilities and it is indeed not too hard to pick unique glyphs for a large subset of alphabets. Rotokas [1] only uses 12 unaccented Latin alphabets for example, so the following would marginally work:

    .@  @@  @@  .@  @.  @@  @@  ..  @.  @@  ..  ..
    @@  @.  .@  .@  @@  @@  @@  @@  @@  .@  @@  @@
    @@  @@  @@  .@  @@  @@  @.  @.  .@  .@  @@  @.
     A   E   g   I   K   O   P   r   S   T   u   v

Maybe you can make the question much more interesting by allowing non-square and/or non-uniform pixels, i.e. segmented displays. That still has a lot of design potentials even to this day.

[1] https://en.wikipedia.org/wiki/Rotokas_language

Technically the binary language of moisture evaporators would be a good example. But for humans, perhaps Quipu/Khipu. Morse code too, I guess.