Remove TypeScript path mappings in favor of relative imports

Fixes https://github.com/xtermjs/xterm.js/issues/5896

TypeScript path mappings for common/*, browser/*, and headless/*
were not rewritten in emitted JavaScript, which forced webpack resolve
aliases and NODE_PATH workarounds so runtime could resolve modules.
That added build complexity and broke tooling such as ESLint import/no-cycle.

Changes:
- Convert ~750 imports across src/, addons/, and test/ to relative paths
- Remove common/browser/headless paths and src catch-all mappings from tsconfigs
  (keep @xterm/addon-* demo and addon typings paths)
- Remove webpack resolve.alias for common, browser, headless, and vs
- Drop NODE_PATH from unit tests, benchmarks, and VS Code launch config
- Fix addon-image IIPImageStorage to import ./Types after removing catch-all *

Verified: npm run build, esbuild, package, package-headless
Co-authored-by: Cursor <cursoragent@cursor.com>

src/common/input/Keyboard.ts

@@ -4,8 +4,8 @@
  * @license MIT
  */
 
-import { IKeyboardEvent, IKeyboardResult, KeyboardResultType } from 'common/Types';
-import { C0 } from 'common/data/EscapeSequences';
+import { IKeyboardEvent, IKeyboardResult, KeyboardResultType } from '../Types';
+import { C0 } from '../data/EscapeSequences';
 
 // reg + shift key mappings for digits and special chars
 const KEYCODE_KEY_MAPPINGS: { [key: number]: [string, string]} = {