Revisit solver verbosity options

At the moment, the "newton" step residuals are printed after each linear solve (for the forward pass), even if the nonlinear solver verbosity is set to 0 whereas the newton residuals are not printed for the backwards pass. LiDO users are requesting a verbosity option that does not print the residuals at all, as well as options to see forward/backwards pass residuals when desired.

Start by tracing where Newton-step residuals are emitted during the forward and backward passes, then inspect how nonlinear solver verbosity is currently handled. Done means users can suppress all residuals or independently request forward and backward residual output, with behavior covered by the relevant solver tests if they exist.

Written by the indexing model from the issue text.