Rebuild IntelliJ project indexes
Solution 1:
File -> Invalidate caches...
(Force rebuild of all caches and indices on next startup)
Restart IntelliJ IDEA.
Caution: This might Remove local history.
Solution 2:
Restarting IntelliJ fixed this in my case (Ultimate 2019.1) -- on restarting, it rebuild the indexes by itself.
An interesting side effect, apart from all imports and non-local references coming up as errors, was the error reported on all string literals:
Incompatible types.
Required: java.lang.String
Found: java.lang.String