I have since contacted Weglot support found the following, for anyone wondering.
The issue turned out to be the following:
I removed the project in Weglot and removed the Squarespace extension.
After adding them back in, I was able to re-select the correct language in the popup menu.
It looks like the language Brazilian Portuguese in Weglot (pt-br) is simply displayed as Breton in Squarespace.
It looks like this is an issue on Squarespace's end.
The issue looks the same as on the earlier screenshots I posted.
When selecting pt-br as a language on Squarespace, the text is indeed not Brazilian Portuguese, but simply looks like English.
As a workaround, I have changed Brazilian Portuguese (pt-br) to Portuguese (pt) for now.
I have requested Weglot support forward the issue to Squarespace devs.