Well, I would differ here. In Germany the curriculum clearly says British English. That does not mean that I learned how to speak like a Scot, but that there is not one Standard English as there is one Standard German.

I recognized huge differences even to the basic materials in Asia which are clearly US English.

(This brings back memories... my first ever English lesson in 5th grade started with: "I am from Hatfield. That's a town in England.")

We phrase things differently because I am a teacher and you work in antoher field. I'll try to reword (Ohne Gewähr):

The linguistic skills are the same whatever version of English you learn. I am talking about language systems here, not a particular vocab or chosen place in school books. When students in English as a foreign language write mixed British/American spelling, you correct it because of system adequacy but you don't take points off for communicative skill, grammar skill or capacity to use complex structures accurately. You just write somewhere a reminder about spelling and that's it. Same with vocab.

To "colour" your English, you need to make conscious linguistic choices about a linguistic system. That is a whole new level of metalanguage: not isolated words from mixed origines are put together but a logical discrimination traits within a system are the base of your metalinguistical reasonning. You do that easily as native speaker, it is a requirement in all sociolinguistic fields, but in the foreign language, it takes quite a level of command of the system, not only of isolated features.

For the exact same sentence spoken, you may have two fundamentally different systemic backgrounds. German example would be a word like "schietig". If you are non native and just heard it on TV, you may repeat it in CH where it does not belong. It's actually a mistake. When I say it, I know very well what I am doing, and that is not a mistake anymore, that's conscious choice of linguage flavouring. The Swiss do that all the time in High German. They can perfectly pronounce durch with a ich-Laut, they don't do it, and their ach-Laut is a Swiss High German marker, belonging to that particular language system. And they like it that way, it's conscious at least on a collective level. On an indidual level, they hear the ach-Laut but don't understand why you tell them that it's against the Bühnendeutsch-rules of the language.

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Es wird nichts ausgelassen, um mich hier herauszuekeln. Ein Lehrbuch. False accusations and attacks continue. There is no stopping righteous people when they are wrong.

I thought this thread was answering a question about the existence of Swiss german Schools.

I teach English but I wouldn't go so far as to say I believe there is anything that we call Standard English.
I did notice that in my child's school in Zurich the pronunciation and vocabulary are taught with a huge bias towards American English by the younger teachers and what I would even consider to be "bad" grammar, problems with uncountables, tapes of songs sung with strong American accents, which is new to me. My child got very blank stares when he used "European English" (inventing my own standard here) vocabulary...

To the original poster: I'd advise learning the basics in German so you can grapple with everyday reading and form-filling and by listening and communicating on the street you can pick up the dialect for free!

Step 1: Learn Standard German

Step 2: Drink Rivella

may be in UNIL you can find a proper class