According to the docs, there should be no limit for the size of item values - but, in reality, there is one…a small one!
After running into trouble trying to save some data, I wrote a successive approximation to find the precise size limit of strings saved as ServerStorage item - and the result was
1048574 (= 1024*1024 - 2)
(trying to save a string of length 1024*1024 - 1 failed)
In my opinion, nowadays, this limit is quite low - and it should definitely be mentioned in the docs (in BOLD) otherwise people may plan apps which they will never get running!
Nota bene: the string I wrote contained ASCII characters only - for non-ASCII characters, the UTF-8 encoding will produce more bytes than the plain string size indicates.