In Switzerland we pretty much lack professional healthcare staff all the time (like half our doctors are from Germany it feels). I'm not working in the industry but afaik nursing is better paid than in Germany, just other conditions around the job are very stressful and make many people leave.
During Covid, things got bad enough that a popular initiative by the trade unions got passed which demanded augmentations to the working conditions. The concrete improvements will soon get voted on and hopefully quickly implemented.
If you already speak German fluently, learning to understand Swiss German will hopefully not be too much of a challenge to you.
Update: I looked it up and a professional nurse makes on average a bit more than median income here.
tbf a big reason for our high share of non-citizens is just that citizenship is much harder to acquire than in most other places