Official EU pet passport is still necessary if you're crossing any borders, and CH is surrounded by EU, dunno what else to tell you.

It's a mess of non-information out there at the expense of (generally) decent pet owners.

These laws are designed to prevent illegal puppy farm style import/export, which is a good thing at least.

And luckily the UK doesn't require the previous quarantines anymore, unlike Australia for example (1 month)

So yeah, it's complicated.. but better to be safe than sorry. Some vets can provide useful info for travel as can airlines but you're better off speaking with an embassy.

To be extra safe ask for email responses and print them to take along - too many good people get turned back at the borders over stupid paperwork, even tho their pet is definitely not ill.

Good luck to all!