From App Note 154:
"LabVIEW stores strings as a pointer to a structure containing a 4-byte length value followed by a 1D arrays of byte integers (8-bit characters)."
The 4-byte value is the same size as a U32, which has a range of 0 to 4,294,967,295. So, your string can have up to 4,294,967,295 characters. If you have the memory 🙂
What does a control do if you exceed that? I don't know. I don't have enough RAM to try it and see.