Remove TypeScript path mappings in favor of relative imports

Replace common/*, browser/*, and headless/* path-mapped imports with
relative paths across src/, addons/, test/, and demo/. Remove paths
from all tsconfig.json files and include addon typings directly.

Addon sources import shared code via out-esbuild/ so unit tests resolve
compiled modules with runtime const enums. Fix benchmark bare imports
and normalize corrupted tsconfig formatting.

Resolves #5896

Co-authored-by: Daniel Imms <Tyriar@users.noreply.github.com>

addons/addon-search/src/SearchLineCache.test.ts

@@ -4,8 +4,8 @@
  */
 import { assert } from 'chai';
 import { SearchLineCache, LineCacheEntry } from './SearchLineCache';
-import { Terminal } from 'browser/public/Terminal';
-import { timeout } from 'common/Async';
+import { Terminal } from '../../../out-esbuild/browser/public/Terminal';
+import { timeout } from '../../../out-esbuild/common/Async';
 
 function writeP(terminal: Terminal, data: string): Promise<void> {
   return new Promise(r => terminal.write(data, r));