You want executable code, so you need to use /e.

s/^([^_]+_).*(\.\w{3})\z/$1 . sprintf("%08d", rand(100000000)) . $2/eg
+;
[download]

or

s/^([^_]+_).*(?=\.\w{3}\z)/$1 . sprintf("%08d", rand(100000000))/eg;
[download]

or (5.10 required)

s/^[^_]+_\K.*(?=\.\w{3}\z)/sprintf("%08d", rand(100000000))/eg;
[download]

This way the files will be unique and uniform for my storage needs.

Random numbers aren't unique. They're random.