What I did: nothing yet
What happened: nothing yet
What I expected: confirmation that if I change where my note sync, I won’t loose anything in the process. Intending to sync from iCloud to Dropbox.
You are allowed to change the cloud service, yes. Just turn off the iCloud sync on each device. It will ask if you want to remove the cloud data. You can choose to do that, or leave it there. Up to you.
Then go and turn on the Dropbox sync on each device. Best to do it one at a time, waiting 20 minutes or so for it to upload. (It should ask you to sign in on each device when you switch to Dropbox. Don’t forget to press the button to go back to the app after sign in.)