Don't emit an error about failing to produce a file with a specific name

If user never gave an explicit name

compiler/rustc_codegen_ssa/src/back/write.rs

@@ -592,7 +592,7 @@ fn produce_final_output_artifacts(
                 .unwrap()
                 .to_owned();
 
-            if crate_output.outputs.contains_key(&output_type) {
+            if crate_output.outputs.contains_explicit_name(&output_type) {
                 // 2) Multiple codegen units, with `--emit foo=some_name`. We have
                 //    no good solution for this case, so warn the user.
                 sess.dcx().emit_warn(errors::IgnoringEmitPath { extension });

compiler/rustc_session/src/config.rs

@@ -557,6 +557,11 @@ impl OutputTypes {
         self.0.contains_key(key)
     }
 
+    /// Returns `true` if user specified a name and not just produced type
+    pub fn contains_explicit_name(&self, key: &OutputType) -> bool {
+        self.0.get(key).map_or(false, |f| f.is_some())
+    }
+
     pub fn iter(&self) -> BTreeMapIter<'_, OutputType, Option<OutFileName>> {
         self.0.iter()
     }

tests/ui/no-explicit-path-issue-122509.rs

@@ -0,0 +1,23 @@
+//@ build-pass
+//@ compile-flags: -C codegen-units=2 --emit asm
+
+fn one() -> usize {
+    1
+}
+
+pub mod a {
+    pub fn two() -> usize {
+        ::one() + ::one()
+    }
+}
+
+pub mod b {
+    pub fn three() -> usize {
+        ::one() + ::a::two()
+    }
+}
+
+fn main() {
+    a::two();
+    b::three();
+}