How do you sync 1 world between Switch and PC on Minecraft Bedrock?

You have to get a realm to do that.

Even if you're just transferring a world between platforms, Microsoft's guide for it requires a realm.

They're not that expensive. I pay about £3/mo for the one I use for my nephew and I regularly switch between mobile and XBox to play on it. The one downside is you have to use Wi-Fi to play a realm on mobile so you can't play on the go.

Edit 1

Actually, there is the free option of leaving one device running at all times. If you create a second account and add yourself as a friend you could leave the PC one on and then join it when you're on the switch. Would mean managing two Steves, though.