Add a few methods to manual & fix doctests (#32417)
* Don't share doctest state between docstrings
This is not, strictly speaking, well defined. There is no official rule
as to which docstring should get executed first.
This will not be supported in a future version of Documenter.
* Add Channel(::Function) to the manual
Also fix the doctest in the docstring. The simpler println variant seems
to be more reliable when printing from a another task (with at-show, the
"Hello" string did not actually get printed).
* Fix Base.splat doctest
The function is not exported. Note that it does not currently get
doctested, but will be tested in a future Documenter version.
* Fix doctest in at-locals docstring
This is not currently included in the manual and therefore not
doctested, but will be in the future.
* Fix doctest in Base.isambiguous docstring
Not currently doctested since it is not included in the manual, but will
be in the future.
* Add findnext/last(::AbstractChar,...) to manual
Also fix a doctest in one of the docstrings.
* Add BLAS.dot and axpby! to manual
And fix the doctests in the docstrings.
* Fix doctests of unexported functions
Fix doctests in the docstrings of LinearAlgebra.isbanded,
LinearAlgebra.promote_leaf_eltypes and SparseArrays.dropstored!. All the
functions are unexported and not included in the manual.
They are currently not being doctested, but will be with a future
version of Documenter.
