Don't filter Core methods from newly-inferred list (#58510)

This allows constructors like `Tuple{Type{Vector{Foo}},
UndefInitializer, Tuple{Int}}` to precompile as usual

Appears to have a minimal effect on the stdlib pkgimages:
```julia
--- before.txt  2025-05-23 08:36:20.171870043 -0400
+++ after.txt   2025-05-22 14:48:49.003869097 -0400
@@ -47,7 +47,7 @@
  20K ../julia/usr/share/julia/compiled/v1.13/Logging/pkgimage.so
  20K ../julia/usr/share/julia/compiled/v1.13/Logging/pkgimage.so
 3.5M ../julia/usr/share/julia/compiled/v1.13/Markdown/pkgimage.so
-3.5M ../julia/usr/share/julia/compiled/v1.13/Markdown/pkgimage.so
+3.6M ../julia/usr/share/julia/compiled/v1.13/Markdown/pkgimage.so
 184K ../julia/usr/share/julia/compiled/v1.13/Mmap/pkgimage.so
 184K ../julia/usr/share/julia/compiled/v1.13/Mmap/pkgimage.so
  28K ../julia/usr/share/julia/compiled/v1.13/MozillaCACerts_jll/pkgimage.so
```

Resolves #58497.

(cherry picked from commit f8ece05)

Author: topolarity

base/compiler/typeinfer.jl

@@ -406,7 +406,7 @@ function cache_result!(interp::AbstractInterpreter, result::InferenceResult)
         code_cache(interp)[linfo] = ci = CodeInstance(interp, result, inferred_result, valid_worlds)
         if track_newly_inferred[]
             m = linfo.def
-            if isa(m, Method) && m.module != Core
+            if isa(m, Method)
                 ccall(:jl_push_newly_inferred, Cvoid, (Any,), ci)
             end
         end

test/precompile.jl

@@ -1854,7 +1854,30 @@ precompile_test_harness("Issue #50538") do load_path
 end
 
 
+precompile_test_harness("Pre-compile Core methods") do load_path
+    # Core methods should support pre-compilation as external CI's like anything else
+    # https://github.com/JuliaLang/julia/issues/58497
+    write(joinpath(load_path, "CorePrecompilation.jl"),
+          """
+          module CorePrecompilation
+          struct Foo end
+          precompile(Tuple{Type{Vector{Foo}}, UndefInitializer, Tuple{Int}})
+          end
+          """)
+    ji, ofile = Base.compilecache(Base.PkgId("CorePrecompilation"))
+    @eval using CorePrecompilation
+    invokelatest() do
+        let tt = Tuple{Type{Vector{CorePrecompilation.Foo}}, UndefInitializer, Tuple{Int}},
+            match = first(Base._methods_by_ftype(tt, -1, Base.get_world_counter())),
+            mi = Base.specialize_method(match)
+            @test isdefined(mi, :cache)
+            @test mi.cache.max_world === typemax(UInt)
+            @test mi.cache.invoke != C_NULL
+        end
+    end
+end
+
 empty!(Base.DEPOT_PATH)
 append!(Base.DEPOT_PATH, original_depot_path)
 empty!(Base.LOAD_PATH)
-append!(Base.LOAD_PATH, original_load_path)
+append!(Base.LOAD_PATH, original_load_path)