The pixel 48,87 in assets/minecraft/textures/font/nonlatin_european.png shouldn't be there as that's a German lowercase Eszett/sharp S (ß, U+00DF), and not a Greek lowercase beta (β, U+03B2). The long tail can be accepted in cursive writing, but that's not the case.
That letter shouldn't have a tail, because the tail makes it look like a Greek β or like a Latin B with a tail.
I've attached both how it could be without that pixel and another proposal compared to B, β, and ẞ.
The three symbols, both uppercase and lowercase, in case you need to copy and paste
| Lowercase | Uppercase |
|---|---|---|
Latin |
|
|
Greek |
|
|
German |
|
|
The proposal
[media]
iirc that pixel was added for better legibility. As you said this is correct in handwriting, so it's not wrong per se.
Also note that there's a gap between the stem and the tail of the ß, which is not the case for β. I'd personally consider that to be the more important differentiating factor.