chore(lint): apply the main eslint config to vue files (#39545)

Vue files only got `eslint-plugin-vue` rules, so stylistic and
TypeScript rules never ran on them, and `import-x` could not see cycles
between `.ts` and `.vue` files.

- Apply the main ESLint config to `.vue` files
- Let `import-x` parse `.vue` files, which surfaced a cycle between
`repo-findfile.ts` and `RepoFileSearch.vue`
- Fix the resulting lint issues

`vue-eslint-parser` is added as a direct dependency because `import-x`
resolves parsers by package name, see
https://github.com/un-ts/eslint-plugin-import-x/issues/381.

web_src/js/components/ViewFileTree.vue

@@ -3,7 +3,7 @@ import ViewFileTreeItem from './ViewFileTreeItem.vue';
 import {onMounted, useTemplateRef, type ShallowRef} from 'vue';
 import {createViewFileTreeStore} from './ViewFileTreeStore.ts';
 
-const elRoot = useTemplateRef('elRoot') as Readonly<ShallowRef<HTMLDivElement>>;;
+const elRoot = useTemplateRef('elRoot') as Readonly<ShallowRef<HTMLDivElement>>;
 
 const props = defineProps({
   repoLink: {type: String, required: true},