Three aspects
First, in Switzerland, while English in the past 50 years moved up heavily, French still has its importance generally, and Italian still is important in fields like construction, craft (craftsmen), all activity in factory workshops plus many services. I do not believe that either French or German have a comparable position in Sweden
Second, many people who live in German speaking Switzerland only have a real command of Standard German, and in regard to the dialect more or less improvise point-to-point wise. That German is fragmented (not only in Switzerland) into so many different dialects (Dialekte, Mundarten, Akzente) may be complicated but is the simple result of a language which only got a bit "unified" by Martin Luther and Johann Wolfgang von Goethe and Emperor Wilhelm II and the Duden Kommission
Third, you mention IT, Telecom, medical, pharma, finance, etc., industries that are traditionally reliant on expats . These industries "traditionally" did NOT depend on immigrants, while factory-workshops, construction-companies, crafts-service-providers, and the waste-disposal-services DID ! The industries you mention only became dependant on immigrants when A) the HQs in Switzerland became much larger than the national economy as such B) the workforce started to decline due to the generation change. But even in those industries, it is not exactly as you describe it. Medical services ? Many doctors and both male and female nurses are from Germany, and have the advantage already to speak the language. Many other people in the medical field will rather speak Italian than English. Yes, finance and IT and Telecom to a heavy extent rely on the English speaking expats. The pharma industry with its centre around Basel however is split between Swiss&Germans, English-speakers and French-speakers
3-b : sizeable immigrants communities like the Kosovari, the Portuguese and the Turks generally are not exactly English speaking but either German or Italian or Italian&German
Let's add that I for two decades made hundreds of phone-calls to the Nordic countries and while at airlines in Iceland and Norway almost everybody spoke English fairly well, I was, in regard to English, not exactly impressed by the Swedes and rather horrified by the Finns. The Danes generally spoke rather German than English (obvious reasons)
I before taking up the job mentioned had heard a lot of what I now see on EF, and no longer believe in the Samichlaus !