chore: move script/ inclusion to TSConfig (#1744)

## PR Checklist

- [x] Addresses an existing open issue: fixes #1743
- [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

💖

eslint.config.js

@@ -52,7 +52,7 @@ export default tseslint.config(
 		languageOptions: {
 			parserOptions: {
 				projectService: {
-					allowDefaultProject: ["*.config.*s", "bin/*.js", "script/*.ts"],
+					allowDefaultProject: ["*.config.*s", "bin/*.js"],
 				},
 				tsconfigRootDir: import.meta.dirname,
 			},

script/__snapshots__/migrate-test-e2e.ts.snap

@@ -174,7 +174,7 @@ exports[`expected file changes > eslint.config.js 1`] = `
  		languageOptions: {
  			parserOptions: {
 -				projectService: {
--					allowDefaultProject: ["*.config.*s", "bin/*.js", "script/*.ts"],
+-					allowDefaultProject: ["*.config.*s", "bin/*.js"],
 -				},
 +				projectService: { allowDefaultProject: ["*.config.*s"] },
  				tsconfigRootDir: import.meta.dirname,
@@ -232,3 +232,15 @@ exports[`expected file changes > knip.json 1`] = `
 +	"project": ["src/**/*.ts!"]
  }"
 `;
+
+exports[`expected file changes > tsconfig.json 1`] = `
+"--- a/tsconfig.json
++++ b/tsconfig.json
+@@ ... @@
+ 		"strict": true,
+ 		"target": "ES2022"
+ 	},
+-	"include": ["src", "script"]
++	"include": ["src"]
+ }"
+`;

script/migrate-test-e2e.ts

@@ -12,6 +12,7 @@ const filesExpectedToBeChanged = [
 	".prettierignore",
 	"cspell.json",
 	"eslint.config.js",
+	"tsconfig.json",
 ];
 
 const filesThatMightBeChanged = new Set([

tsconfig.json

@@ -12,5 +12,5 @@
 		"strict": true,
 		"target": "ES2022"
 	},
-	"include": ["src"]
+	"include": ["src", "script"]
 }