chore(website): auto-generate type checked rule notice in rule docs (typescript-eslint#7951)

* chore(website): auto-generate type checked rule notice in rule docs

* Remove called-out now-unnecessary blips

* fix /troubleshooting/performance-troubleshooting link

* Standardized insertion helper naming, and added to a folder

* Consolidated into a utils.ts file

* Add a thematic line break after existing content

* Refactored into a class

* Update packages/website/plugins/generated-rule-docs/index.ts

Author: JoshuaKGoldberg

.cspell.json

@@ -137,7 +137,6 @@
     "unfixable",
     "unoptimized",
     "unprefixed",
-    "upcasting",
     "upsert",
     "warnonunsupportedtypescriptversion",
     "Zacher"

packages/eslint-plugin/docs/rules/no-unnecessary-condition.md

@@ -101,8 +101,7 @@ You might consider using [ESLint disable comments](https://eslint.org/docs/lates
 This rule has a known edge case of triggering on conditions that were modified within function calls (as side effects).
 It is due to limitations of TypeScript's type narrowing.
 See [#9998](https://github.com/microsoft/TypeScript/issues/9998) for details.
-
-We recommend upcasting the variable with a [type assertion](https://www.typescriptlang.org/docs/handbook/2/everyday-types.html#type-assertions).
+We recommend using a [type assertion](https://www.typescriptlang.org/docs/handbook/2/everyday-types.html#type-assertions) in those cases.
 
 ```ts
 let condition = false as boolean;