Crack theory: Blue is actually from Bavaria. Proof:
Flag of Bavaria
Alright —
So according to wikipedia, Bavaria has two equally official flags: the ones with the lozenge like you showed and a simple blue and white striped flag.
The other picture comes from the blog @blueoctobass (note that the header is only visible on mobile).
One of the main difference is the color used.
@blueoctobass is a fanblog run by @papier-ciseaux (as mentioned here) and if you dig far enough in the archives, you can see that this background is used in a drawing from July 2019. Blueoctobass reblogged its first posts in February 2020, so the timeline is this: the background is created in July 2019 and later used as a header for a blue-themed blog because it fits the aesthetic.
Okay, so that sounds like one big coincidence.
It's also a fanblog.
HOWEVER!
An old (3rd July 2017) by CQ states that : "Ecoversians have Australian accents, Stratoversians have British, I have no clue about Inverse but I think thats neat"
This is to be taken with a spoon of salt since it's old and CQ has recently asked people to not take old posts as proof.
It can still give us a direction. So Bavaria is a Land of Germany, not of Australia or Britain, but Germany and Britain both have a certain saxon heritage in common (England and Germany have both trespassed into each other territory a fair amount of time in the past and thus have a lot of words in common in their respective languages).
Stratoverse is a country, one of the five major ones existing on Gloomball. They can have multiple accents. Let's say that the "British" accent is more of a "Northern European" accent.
This would mean that a "Bavarian Blue" would be equal to a Stratoversian Blue.
We have no information on whether she was born in Gloomverse or fled to it like Indigo did, but she is much more well adjusted than him and doesn't stand out nearly as much (many people theorised that Indigo was either Stratoversian or Inversian based on his look).
Blue is very formal and worried about appearances and conduct, as well as "being dangerous", which could stem from an upbringing in the controlling Stratoverse rather than the exuberant Gloomverse. She has a sister, Cakegirl, but she seems to be the younger of the two. It's also worth noting that Cakegirl is/was a very powerful magician, and characters are impressed by her golem.
And.... statically speaking, that could mean she is Stratoversian!
It is possible that Blue was born in Stratoverse and fled towards Gloomverse, either with her parents (Cakegirl being born in Gloomverse or too young to remember Stratoverse) or without them (She got adopted by Cakegirl's parents which may be a reason why Cakegirl is hostile towards her).
We don't know how or why random people get turned into colors, but Green and Alpha Green are both Ecoversian, its possible that Alpha Blue was Stratoversian and so current Blue is also Stratoversian.
Purple would be an outlier since Violet was likely Stratoversian and yet he was born in Steamverse.
TL;DR: While the flag of bavaria on someone's fanblog isn't much of a proof, Blue could still be as close to bavarian as we can do in a fictional world by being Stratoversian. Stratoverse is supposedly British/North-European and thus German. There is no proof against Blue being Stratoversian and it could explain the difference between her and Cakegirl (difference of upbringing) while also explaining why Cakegirl was so powerful.