Recently the Google keyboard has activated suggestions for both of my selected languages. This is a real nuisance since the suggestions are a mess IMO.
How can I disable it and go back to switching languages manually?
As you've mentioned, the multilingual suggestions is a new feature in Gboard (ref: Gboard, now available for Android - Official Google Blog.
Steps to enable/disable it:
Note: the preference is not symmetric. When you have 2 languages that are supported for multilingual typings, you can disable it on language A while having it enabled on language B with A.
How can I get back to manually switching between languages? Is there a setting I've missed, or do I have to roll back to an earlier version?
On the the keyboard options you'll find settings for Languages, Preferences, Theme... and in Text correction you'll find the toggle you're looking for: multilingual typing.
In the latest versions of gboard the multilingual settings have moved to the Languages submenu which can be quickly accessed by long tapping the SPACE key, and then picking LANGUAGE SETTINGS in the popup that appears (at the very bottom, below the language list).
Now, tap each language one by one, and uncheck the multilingual typing option.
You can also access the Languages menu from settings:
Go to Settings > Languages & Input > Virtual keyboard > gboard > Languages