fix(migrate-eslint): load non-conventional shared config name (#4538)

CHANGELOG.md

@@ -27,6 +27,15 @@ our [guidelines for writing a good changelog entry](https://github.com/biomejs/b
 - `biome migrate eslint` now correctly resolves scoped package named `eslint-config` with a path.
   Contributed by @Conaclos
 
+- `biome migrate eslint` now correctly handles shared ESLint configuration that don't follow the ESLint naming convention ([#4528](https://github.com/biomejs/biome/issues/4528)).
+
+  ESLint recommends that a package that exports a shared configuration be prefixed with `eslint-config-` or simply named `eslint-config`.
+  This is only a recommendation.
+  Packages that export shared configurations can have arbitrary names.
+  Biome is now able to load any package.
+
+  Contributed by @Conaclos
+
 ### Configuration
 
 ### Editors

crates/biome_cli/src/execute/migrate/eslint.rs

@@ -308,10 +308,17 @@ fn load_eslint_extends_config(
         } else {
             EslintPackage::Config.resolve_name(name)
         };
+        // Try to load `module_name` or else try to load diretcly `name`.
         let node::Resolution {
             content,
             resolved_path,
-        } = node::load_config(&module_name)?;
+        } = node::load_config(&module_name).or_else(|err| {
+            if module_name != name {
+                node::load_config(name)
+            } else {
+                Err(err)
+            }
+        })?;
         let deserialized = deserialize_from_json_str::<eslint_eslint::LegacyConfigData>(
             &content,
             JsonParserOptions::default(),