As well as endorsing Robert Harvey's word "populated", I'd like to suggest the words
replete or even
impleted as the opposite of empty.
Although these words are more or less a synonym of "full", and perhaps even over-fullness and excess, in this context they're far more unusual words than "full" with fewer connotations of wholeness or limited capacity, and a stronger connotation of there being a complement of one or more individual items present (which is the same connotation that "populated" carries).
For example, you can use "full" like "he ate a full cake", which means the entirety of a single cake, not multiple cakes. Or "the dungeon was full" strongly suggests that it has reached its capacity, not that it is merely populated. These are connotations which make it unsuitable to talk of a "full string", which can be as little as one character or an indefinite number of characters.
They're also snappy words and not needlessly long to write or pronounce.
I seem to remember a similar question arising recently, and should I myself encounter a need to describe something (a container, array, string, etc.) that is "nonempty", I think "replete" may well be the word I turn to.
Correspondingly, I could well envisage myself generically describing a string that consists only either of a null, an empty string, or whitespace, as "nonreplete".