Is there a standard prefix random padding scheme? Is there a standardized padding scheme which is prefix instead of postfix
and that uses random bytes except for the first byte which would be the
length of the padding?
I know of no standard like that and also doubt it exists.

It would have similar disadvantages as random padding at the end, which is no longer in use: subliminal channel, consumption of randomness which may be expensive. Additionally, it would require knowing the message length in advance, which is a practical limitation.