It keep track of the size of the buffer and the number of bytes therein.
$ perl -MDevel::Peek -e'$x="abcdefghij"; Dump($x);'
SV = PV(0x9222b00) at 0x9222678
REFCNT = 1
FLAGS = (POK,pPOK)
PV = 0x9238220 "abcdefghij"\0
CUR = 10 <-- 10 bytes used
LEN = 12 <-- 12 bytes allocated
On a 32-bit build of Perl, it uses 32-bit unsigned integer for these values. This is (exactly) large enough to create a string that uses up your process's entire 4 GiB address space.
On a 64-bit build of Perl, it uses 64-bit unsigned integer for those values. This is (exactly) large enough to create a string that uses up your process's entire 16 EiB address space.
The docs are correct. The size of the string is limited only by available memory.