If you could demonstrate, prove or explain why water speed should
be identical along each side of the rudder

water speed does not have to be equal or greater or less. This can be a bit
confusing because "bernoulli" is often -- though erroneously -- given as the
reason sails/wings have "lift".

It might be a bit easier to remember that for the rudder to be pushed one way,
it (the rudder) must push water the opposite way. If the water is not
deflected then there is no force on the rudder.

I mentioned Feynman because some clowns on this ng (I speak of schlackoff and
jeffies and others) go ape squat when I make a statement, absolutely insisting
that if I say it I must be making it up (I make up nothing) will argue for
weeks (like sophomores in college wasting afternoons in the student cafeteria
as they consider their fourth or fifth major) to prove because they didn't know
something prior, no one else could have either.

Feynman, a serious physicist, got sick and tired of arguing with the 4th major
sophomore types and made a movie of the situation, showing clearing exactly
what was expected. I used Feynman's name to shut up schlackoff (fat chance)
and jeffies (who became quiet once he goggled the name Feynman).

I mentioned the whole issue because I have met boaters who, when the complained
about troubles backing up their ruddered boat, had unscrupulous marinas try to
sell them a multi-thousand dollar "solution" to the problem by "moving the prop
closer to the rudder for better control". Which won't work, of course.