Add test for #38149 (#41958)

No code change is needed, but the use-case in that issue doesn't
appear to be tested directly.

Closes #38149

test/precompile.jl

@@ -875,3 +875,19 @@ precompile_test_harness("Renamed Imports") do load_path
  Base.compilecache(Base.PkgId("RenameImports"))
  @test (@eval (using RenameImports; RenameImports.test())) isa Module
 end
+
+@testset "issue 38149" begin
+ M = Module()
+ @eval M begin
+ @nospecialize
+ f(x, y) = x + y
+ f(x::Int, y) = 2x + y
+ end
+ precompile(M.f, (Int, Any))
+ precompile(M.f, (AbstractFloat, Any))
+ mis = map(methods(M.f)) do m
+ m.specializations[1]
+ end
+ @test any(mi -> mi.specTypes.parameters[2] === Any, mis)
+ @test all(mi -> isa(mi.cache, Core.CodeInstance), mis)
+end