fix: fix incorrect metadata handling in symbolic affect simplification

Author: AayushSabharwal

src/structural_transformation/symbolics_tearing.jl

@@ -972,7 +972,10 @@ function update_simplified_system!(
         # Algebraic variables are shifted forward by one, so we backshift them.
         unknowns = map(enumerate(unknowns)) do (i, var)
             if iscall(var) && operation(var) isa Shift && operation(var).steps == 1
-                backshift_expr(var, iv)
+                # We might have shifted a variable with io metadata. That is irrelevant now
+                # because we handled io variables earlier in `_mtkcompile!` so just ignore
+                # it here.
+                setio(backshift_expr(var, iv), false, false)
             else
                 var
             end

test/symbolic_events.jl

@@ -1410,3 +1410,12 @@ end
     sol = solve(prob, FBDF())
     @test SciMLBase.successful_retcode(sol)
 end
+
+@testset "Algebraic equation with input variable in symbolic affect" begin
+    # Specifically happens when the variable marked as an input is an algebraic variable
+    # in the affect system.
+    @variables x(t) [input = true] y(t)
+    dev = ModelingToolkit.SymbolicDiscreteCallback(1.0, [y ~ Pre(y) + 1])
+    @named sys = System([D(y) ~ 2x + 1, x^2 ~ 2y^3], t; discrete_events = [dev])
+    sys = @test_nowarn mtkcompile(sys)
+end