fix: remove package.json packageManager field (#1529)

## PR Checklist

- [x] Addresses an existing open issue: fixes #1513
- [x] That issue was marked as [`status: accepting
prs`](https://github.com/JoshuaKGoldberg/create-typescript-app/issues?q=is%3Aopen+is%3Aissue+label%3A%22status%3A+accepting+prs%22)
- [x] Steps in
[CONTRIBUTING.md](https://github.com/JoshuaKGoldberg/create-typescript-app/blob/main/.github/CONTRIBUTING.md)
were taken

## Overview

Right now, trying to use `create-typescript-app` with anything but the
_exact correct pnpm major.minor.patch version_ installed produces an
error. That's very annoying.

Pending nodejs/corepack#95, removes usage of
the [experimental `package.json` `packageManager`
field](https://nodejs.org/api/packages.html#packagemanager).

Author: JoshuaKGoldberg

.github/actions/prepare/action.yml

@@ -5,6 +5,8 @@ name: Prepare
 runs:
   steps:
     - uses: pnpm/action-setup@v2
+      with:
+        version: 9
     - uses: actions/setup-node@v4
       with:
         cache: pnpm

package.json

@@ -100,7 +100,6 @@
 		"typescript-eslint": "^7.7.0",
 		"vitest": "^1.4.0"
 	},
-	"packageManager": "[email protected]",
 	"engines": {
 		"node": ">=18"
 	},

src/steps/writing/creation/dotGitHub/actions.test.ts

@@ -15,6 +15,8 @@ name: Prepare
 runs:
   steps:
     - uses: pnpm/action-setup@v2
+      with:
+        version: 9
     - uses: actions/setup-node@v4
       with:
         cache: pnpm

src/steps/writing/creation/dotGitHub/actions.ts

@@ -9,7 +9,10 @@ export function createDotGitHubActions() {
 					name: "Prepare",
 					runs: {
 						steps: [
-							{ uses: "pnpm/action-setup@v2" },
+							{
+								uses: "pnpm/action-setup@v2",
+								with: { version: 9 },
+							},
 							{
 								uses: "actions/setup-node@v4",
 								with: { cache: "pnpm", "node-version": "20" },

src/steps/writing/creation/writePackageJson.test.ts

@@ -91,7 +91,6 @@ describe("writePackageJson", () => {
 			  },
 			  "main": "./lib/index.js",
 			  "name": "test-repository",
-			  "packageManager": "[email protected]",
 			  "publishConfig": {
 			    "provenance": true,
 			  },
@@ -162,7 +161,6 @@ describe("writePackageJson", () => {
 			  },
 			  "main": "./lib/index.js",
 			  "name": "test-repository",
-			  "packageManager": "[email protected]",
 			  "publishConfig": {
 			    "provenance": true,
 			  },

src/steps/writing/creation/writePackageJson.ts

@@ -75,7 +75,6 @@ export async function writePackageJson(options: Options) {
 		},
 		main: "./lib/index.js",
 		name: options.repository,
-		packageManager: "[email protected]",
 		publishConfig: {
 			provenance: true,
 		},