Fix handle_dt! for discrete solvers and backward compat

The two-arg handle_dt!(integrator, dt) must also check
iszero(integrator.dt) before auto-resetting, since discrete
solvers set _dt=1 even when dt=nothing.

Also preserve the original one-arg handle_dt! with the old
iszero(integrator.dt) check for backward compatibility with
DelayDiffEq and other packages.

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

Author: claude

lib/OrdinaryDiffEqCore/src/solve.jl

@@ -711,9 +711,26 @@ end
 
 # Helpers
 
-handle_dt!(integrator) = handle_dt!(integrator, nothing)
+function handle_dt!(integrator)
+    return if iszero(integrator.dt) && integrator.opts.adaptive
+        auto_dt_reset!(integrator)
+        if sign(integrator.dt) != integrator.tdir && !iszero(integrator.dt) &&
+                !isnan(integrator.dt)
+            error("Automatic dt setting has the wrong sign. Exiting. Please report this error.")
+        end
+        if isnan(integrator.dt)
+            @SciMLMessage(
+                "Automatic dt set the starting dt as NaN, causing instability. Exiting.",
+                integrator.opts.verbose, :dt_NaN
+            )
+        end
+    elseif integrator.opts.adaptive && integrator.dt > zero(integrator.dt) &&
+            integrator.tdir < 0
+        integrator.dt *= integrator.tdir # Allow positive dt, but auto-convert
+    end
+end
 function handle_dt!(integrator, dt)
-    return if isnothing(dt) && integrator.opts.adaptive
+    return if isnothing(dt) && iszero(integrator.dt) && integrator.opts.adaptive
         auto_dt_reset!(integrator)
         if sign(integrator.dt) != integrator.tdir && !iszero(integrator.dt) &&
                 !isnan(integrator.dt)