I see you are moving the goalposts. Your original statement only said mutation is random. You now add “with respect to fitness”.
Please explain how this is significantly different.
Explain how a pair of dice that is "truly random" is different from a pair of dice that is merely random with respect to winning or losing.
There might be a philosophical difference, but not a difference that can be detected by mere mortals.
All the philosophizing is irrelevant, because what experiment shows is that mutation produces all possible combinations of change. Even if mutations occurred in some kind of alphabetical order, the outcome would be the same. Those that are neutral or favorable will show up more frequently in subsequent generations.