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/public/BufferApiView.ts

@@ -4,9 +4,9 @@
  */
 
 import { IBuffer as IBufferApi, IBufferLine as IBufferLineApi, IBufferCell as IBufferCellApi } from '@xterm/xterm';
-import { IBuffer } from 'common/buffer/Types';
-import { BufferLineApiView } from 'common/public/BufferLineApiView';
-import { CellData } from 'common/buffer/CellData';
+import { IBuffer } from '../buffer/Types';
+import { BufferLineApiView } from './BufferLineApiView';
+import { CellData } from '../buffer/CellData';
 
 export class BufferApiView implements IBufferApi {
   constructor(

src/common/public/BufferLineApiView.ts

@@ -3,8 +3,8 @@
  * @license MIT
  */
 
-import { CellData } from 'common/buffer/CellData';
-import { IBufferLine, ICellData } from 'common/Types';
+import { CellData } from '../buffer/CellData';
+import { IBufferLine, ICellData } from '../Types';
 import { IBufferCell as IBufferCellApi, IBufferLine as IBufferLineApi } from '@xterm/xterm';
 
 export class BufferLineApiView implements IBufferLineApi {

src/common/public/BufferNamespaceApi.ts

@@ -4,10 +4,10 @@
  */
 
 import { IBuffer as IBufferApi, IBufferNamespace as IBufferNamespaceApi } from '@xterm/xterm';
-import { BufferApiView } from 'common/public/BufferApiView';
-import { ICoreTerminal } from 'common/Types';
-import { Disposable } from 'common/Lifecycle';
-import { Emitter } from 'common/Event';
+import { BufferApiView } from './BufferApiView';
+import { ICoreTerminal } from '../Types';
+import { Disposable } from '../Lifecycle';
+import { Emitter } from '../Event';
 
 export class BufferNamespaceApi extends Disposable implements IBufferNamespaceApi {
   private _normal: BufferApiView;

src/common/public/ParserApi.ts

@@ -3,9 +3,9 @@
  * @license MIT
  */
 
-import { IParams } from 'common/parser/Types';
+import { IParams } from '../parser/Types';
 import { IDisposable, IFunctionIdentifier, IParser } from '@xterm/xterm';
-import { ICoreTerminal } from 'common/Types';
+import { ICoreTerminal } from '../Types';
 
 export class ParserApi implements IParser {
   constructor(private _core: ICoreTerminal) { }

src/common/public/UnicodeApi.ts

@@ -3,7 +3,7 @@
  * @license MIT
  */
 
-import { ICoreTerminal } from 'common/Types';
+import { ICoreTerminal } from '../Types';
 import { IUnicodeHandling, IUnicodeVersionProvider } from '@xterm/xterm';
 
 export class UnicodeApi implements IUnicodeHandling {