What happens to my Apple One subscription if I change country

To put it bluntly and in a very non-Apple manner (I can do this because I don't work for them, otherwise they would tell you the same, just with nicer phrasing), you lose all content. Deep down in the legal documents: https://www.apple.com/legal/internet-services/itunes/us/terms.html you will find, "When your Paid Subscription to any Service ends, you will lose access to any functionality or Content of that Service that requires a Paid Subscription."

This article describes how to change your country setting on everything using your Apple ID and the requirements and results of doing this: Read how to "Change your Apple ID country or region", click here --> https://support.apple.com/HT201389

One requirement is you cancel all subscriptions.

Basically you will need to cancel the subscription before you can change countries, and then wait for it to expire.

Then change the country set for all the Apple IDs involved, and then re-subscribe to Apple One.

When you cancel the subscriptions, unfortunately all content may be lost, so make sure you download any data in iCloud you want to keep and that exceeds the free 5GB iCloud option from all accounts. As anything exceeding 5GB will be deleted from iCloud during the change over.

Apple Music playlists and songs unfortunately will be lost during the change and there's no way to keep them as content is country dependent.

Also make sure you download any purchases made through the Swiss based accounts to a device or computer as they may not be available once you change countries.

Not necessarily since it is a new subscription. The iCloud syncing should bring it back.