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/browser/input/CompositionHelper.test.ts

@@ -4,9 +4,9 @@
  */
 
 import { assert } from 'chai';
-import { CompositionHelper } from 'browser/input/CompositionHelper';
-import { MockRenderService } from 'browser/TestUtils.test';
-import { MockCoreService, MockBufferService, MockOptionsService } from 'common/TestUtils.test';
+import { CompositionHelper } from './CompositionHelper';
+import { MockRenderService } from '../TestUtils.test';
+import { MockCoreService, MockBufferService, MockOptionsService } from '../../common/TestUtils.test';
 
 describe('CompositionHelper', () => {
   let compositionHelper: CompositionHelper;

src/browser/input/CompositionHelper.ts

@@ -3,9 +3,9 @@
  * @license MIT
  */
 
-import { IRenderService } from 'browser/services/Services';
-import { IBufferService, ICoreService, IOptionsService } from 'common/services/Services';
-import { C0 } from 'common/data/EscapeSequences';
+import { IRenderService } from '../services/Services';
+import { IBufferService, ICoreService, IOptionsService } from '../../common/services/Services';
+import { C0 } from '../../common/data/EscapeSequences';
 
 interface IPosition {
   start: number;

src/browser/input/Mouse.test.ts

@@ -5,7 +5,7 @@
 
 import jsdom = require('jsdom');
 import { assert } from 'chai';
-import { getCoords } from 'browser/input/Mouse';
+import { getCoords } from './Mouse';
 
 const CHAR_WIDTH = 10;
 const CHAR_HEIGHT = 20;

src/browser/input/MoveToCell.test.ts

@@ -4,8 +4,8 @@
  */
 
 import { assert } from 'chai';
-import { IBufferService } from 'common/services/Services';
-import { MockBufferService } from 'common/TestUtils.test';
+import { IBufferService } from '../../common/services/Services';
+import { MockBufferService } from '../../common/TestUtils.test';
 import { moveToCellSequence } from './MoveToCell';
 
 describe('MoveToCell', () => {

src/browser/input/MoveToCell.ts

@@ -3,8 +3,8 @@
  * @license MIT
  */
 
-import { C0 } from 'common/data/EscapeSequences';
-import { IBufferService } from 'common/services/Services';
+import { C0 } from '../../common/data/EscapeSequences';
+import { IBufferService } from '../../common/services/Services';
 
 const enum Direction {
   UP = 'A',