chore(web): reduce lint duration by 90% (#1766)

Replace the eslint prettier plugin (which profiling revealed to be the
bottleneck) with separate `prettier` invocations. This yielded a 73 second reduction (89%) in the environment described below.

Before:
```
pnpm --filter web lint:fix  81.79s user 1.85s system 110% cpu 1:15.81 total
```
After: 
```
pnpm --filter web lint:fix  8.83s user 0.93s system 170% cpu 5.737 total
```
System specs (Nov 5 2025):
```
OS: macOS Sequoia 15.6.1 (24G90) arm64
Host: MacBook Air (15-inch, M2, 2023)
Kernel: Darwin 24.6.0
Uptime: 44 days, 5 hours, 22 mins
Packages: 52 (nix-default), 195 (brew), 4 (brew-cask)
Shell: zsh 5.9
CPU: Apple M2 (8) @ 3.50 GHz
GPU: Apple M2 (10) @ 1.40 GHz [Integrated]
Memory: 19.51 GiB / 24.00 GiB (81%)
Swap: 4.83 GiB / 6.00 GiB (80%)
```

<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->

## Summary by CodeRabbit

* **Chores**
* Separated code formatting and linting tools into independent workflows
for improved developer efficiency
* Updated development tool configuration to streamline the linting and
formatting process

<!-- end of auto-generated comment: release notes by coderabbit.ai -->

Author: pujitm

pnpm-lock.yaml

@@ -0,0 +1,4 @@
+auto-imports.d.ts
+components.d.ts
+composables/gql/
+src/composables/gql/

web/.prettierignore

@@ -1,7 +1,6 @@
 import eslint from '@eslint/js';
 import importPlugin from 'eslint-plugin-import';
 import noRelativeImportPaths from 'eslint-plugin-no-relative-import-paths';
-import prettier from 'eslint-plugin-prettier';
 import vuePlugin from 'eslint-plugin-vue';
 import globals from 'globals';
 import tseslint from 'typescript-eslint';
@@ -23,7 +22,6 @@ const commonRules = {
     'error',
     { allowSameFolder: false, rootDir: 'src', prefix: '@' },
   ],
-  'prettier/prettier': 'warn',
   'no-restricted-globals': [
     'error',
     {
@@ -115,7 +113,6 @@ export default [
     },
     plugins: {
       'no-relative-import-paths': noRelativeImportPaths,
-      prettier: prettier,
       import: importPlugin,
     },
     rules: {
@@ -141,7 +138,6 @@ export default [
     },
     plugins: {
       'no-relative-import-paths': noRelativeImportPaths,
-      prettier: prettier,
       import: importPlugin,
       vue: vuePlugin,
     },
@@ -174,7 +170,6 @@ export default [
     },
     plugins: {
       'no-relative-import-paths': noRelativeImportPaths,
-      prettier: prettier,
     },
     rules: {
       ...commonRules,

web/eslint.config.mjs

@@ -23,8 +23,11 @@
     "clean-unraid": "./scripts/clean-unraid.sh",
     "copy-to-webgui-repo": "./scripts/copy-to-webgui-repo.sh",
     "// Code Quality": "",
-    "lint": "eslint .",
-    "lint:fix": "eslint . --fix",
+    "lint": "pnpm lint:eslint && pnpm lint:prettier",
+    "lint:eslint": "eslint --cache",
+    "lint:prettier": "prettier --check \"**/*.{js,ts,tsx,vue}\"",
+    "lint:fix": "pnpm exec eslint --cache --fix . && pnpm prettier:write",
+    "prettier:write": "prettier --write \"**/*.{js,ts,tsx,vue}\"",
     "type-check": "vue-tsc --noEmit",
     "clean": "rm -rf dist dist-wc",
     "// GraphQL Codegen": "",
@@ -68,7 +71,6 @@
     "eslint-import-resolver-typescript": "4.4.4",
     "eslint-plugin-import": "2.32.0",
     "eslint-plugin-no-relative-import-paths": "1.6.1",
-    "eslint-plugin-prettier": "5.5.4",
     "eslint-plugin-storybook": "9.1.3",
     "eslint-plugin-vue": "10.4.0",
     "glob": "11.0.3",