I am trying to figure out whether it is possible for a Salesforce field to switch from one global picklist into another? Trying to click around but didn't find the option
Funny you should ask this as we were trying this just today...
The answer is NO; from the Help doc
You can’t undo a custom picklist field’s association with a global value set. If you need a picklist field to use a different global value set, or different individual values, delete the custom picklist field and create a new one in its place.
Side note: You can rename the global value set and the custom field(s) that use it will automatically change to the new reference - but deploying that can't be done with the metadata API