Can this even return anything else since 5.20? Consistent RNG

Looks like not - and thanks for pointing that out.
But the main thing is that $Config{randbits} accurately tells us just how many random bits there are in the values returned by rand().
And, on Strawberry Perl 5.38.2, that seems to be the case:

D:\>perl -MMath::MPFR=":mpfr" -le "for(1..10) { Rmpfr_dump(Math::MPFR-
+>new(rand())) }"
0.10111101010110010000010001100010101000100000001000000E-1
0.10101011001001100100100010110010011000110111100000000E0
0.11101100101010101111101111110010001010100010001100000E0
0.11110011010000100001010001110110110001011110010000000E-1
0.10101100000100111001001010001101000110100010101000000E-1
0.11101001110010110101101100100110111011111111110000000E0
0.10111011011010001000111110000000100101100101011100000E0
0.11110010000111110101011000001100010110100010110000000E-1
0.10000101100011000000001001101010111101100110100100000E0
0.11100110010000001010111101110010100000011000000000000E-1
[download]

Note that the last 5 bits are always 0.

The remaining question is: "How many random bits is random() providing ?"

Cheers,
Rob