ENH: optimize.root_scalar: allow newton without f', secant without x1

[mdhaber]

Reference issue

Closes gh-17570

What does this implement/fix?

root_scalar does not allow method='newton' to be used without an analytical derivative even though scipy.optimize.root does, and it does not allow method='secant' to be used without an explicit x1 even though scipy.optimize.newton does. This PR removes root_scalar's restrictions on use of these methods and updates the defaults method resolution accordingly.

Additional information

I don't think there are any BC concerns because it is documented that

[mdhaber]

No test failed (because of this PR) after the second commit, and the last commit made a minor tweak to the documentation, so I skipped CI.

[tupui]

LGTM, thanks Matt 👍

@andyfaff do you have comments?

I would merge in 2 weeks otherwise.

[mdhaber]

@andyfaff looks like this might merge, but still let us know if there's an issue. There's plenty of time to change it before the next release.

[tupui]

Merging tomorrow.