Why PS does differ between PKCS1 v1.5 padding for signature and for encryption?
Maarten Bodewes answer is correct, but it is missing one important point.

It is actually NOT secure to have randomness in PKCS#1V1.5 padded signatures, otherwise signatures could be forged via bleichenbacher's e=3 attack.

Take a look at https://blog.filippo.io/bleichenbacher-06-signature-forgery-in-python-rsa/ to see what happens when signature verification implementations forget to assert that those bytes are actually 0xFF.