All your data stays on your device. You only upload your random identifier if you test positive, as confirmed by a trusted health provider. I would worry much more about them if I were you. Personally I'm far more concerned about dying from COVID-19 than the government who already knows much about me abuses my health status of this virus.
I lived in Switzerland, paid 12% taxes and 5% for AHV (public pension fund, you don't get this money back), lived in a 100sqm (1000sqf) flat for 1800 chf a month, 25 min to zurich by train but only a 15min bike ride to work, ~110k salary
You can get a work visa if a Swiss company wants to hire you for a special skill or expertise you have. The easier way is probably to start working for a Swiss company in the US and then let you relocate to Switzerland still working for that company.
It's not really about US citizenship. It's about being subject to US taxation. The IRS has a rather more generous definition of whether you are a "US person" than the INS does.
That said, if you are a legal resident in Switzerland, you should be able to find banking here. If you just step off the plane with a suitcase full of money and walk into a bank, though — I would recommend making it a LARGE suitcase.
FWIW I am not a US citizen but had to fill out an IRS tax form as well when getting a bank account in Switzerland since I was living in the US for 5 years.