Is your feature request related to a problem or challenge?

Part of #8913

While working on the documentation in #10035, @peter-toth made the great observation #10035 (comment) that:

I have no idea why we have the ..._mut() version, most likely for just convenience, but IMO one transform_down() with FnMut should be fair enough.

Specifically, these methods are basically the same, except that _mut takes a mutable reference to the closure

• transform_down / transform_down_mut
• transform_up / transform_up_mut

The current API is pretty confusing enough already (see discussion on #10035) so having redundant methods just makes it more confusing

Also, this terminology leaked into the LogicalPlan variants transform_down_with_subqueries_mut etc in #9913

Describe the solution you'd like

I would like to deprecate

• transform_down_mut
• transform_up_mut

And remove the (yet unreleased) logical plan variants transform_down_with_subqueries_mut and transform_up_with_subqueries_mut

Describe alternatives you've considered

No response

Additional context

No response