Use silent linear verbosity by default to avoid BLAS errors

Change the default linear_verbosity from Minimal() to None() in
NonlinearVerbosity to prevent BLAS errors from being emitted when
the linear solver encounters singular matrices. These errors are
not fatal in the nonlinear solver context since the solver
handles singular matrices gracefully by falling back to QR.

Fixes #739

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

Author: ChrisRackauckas

lib/NonlinearSolveBase/src/verbosity.jl

@@ -132,8 +132,10 @@ function NonlinearVerbosity(;
     end
 
     # Build arguments using NamedTuple for type stability
+    # Use None() for linear_verbosity by default since BLAS errors are not fatal
+    # in the nonlinear solver context (the solver handles singular matrices gracefully)
     default_args = (
-        linear_verbosity = linear_verbosity === nothing ? Minimal() : linear_verbosity,
+        linear_verbosity = linear_verbosity === nothing ? None() : linear_verbosity,
         non_enclosing_interval = WarnLevel(),
         alias_u0_immutable = WarnLevel(),
         linsolve_failed_noncurrent = WarnLevel(),
@@ -167,8 +169,10 @@ end
 function NonlinearVerbosity(verbose::AbstractVerbosityPreset)
     if verbose isa Minimal
         # Minimal: Only fatal errors and critical warnings
+        # Use None() for linear_verbosity since BLAS errors are not fatal
+        # in the nonlinear solver context (the solver handles singular matrices gracefully)
         NonlinearVerbosity(
-            linear_verbosity = Minimal(),
+            linear_verbosity = None(),
             non_enclosing_interval = WarnLevel(),
             alias_u0_immutable = Silent(),
             linsolve_failed_noncurrent = WarnLevel(),