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>

test/playwright/Terminal.test.ts

@@ -5,7 +5,7 @@
 import { test } from '@playwright/test';
 import { deepStrictEqual, notStrictEqual, strictEqual } from 'assert';
 import { ITestContext, createTestContext, openTerminal, pollFor, timeout } from './TestUtils';
-import { IRenderDimensions } from 'browser/renderer/shared/Types';
+import { IRenderDimensions } from '../../src/browser/renderer/shared/Types';
 
 let ctx: ITestContext;
 test.beforeAll(async ({ browser }) => {

test/playwright/TestUtils.ts

@@ -5,9 +5,9 @@
 
 import { Browser, JSHandle, Page } from '@playwright/test';
 import { deepStrictEqual, strictEqual } from 'assert';
-import type { IRenderDimensions as IRenderDimensionsInternal } from 'browser/renderer/shared/Types';
-import type { IRenderService } from 'browser/services/Services';
-import type { ICoreTerminal, IDisposable, IMarker } from 'common/Types';
+import type { IRenderDimensions as IRenderDimensionsInternal } from '../../src/browser/renderer/shared/Types';
+import type { IRenderService } from '../../src/browser/services/Services';
+import type { ICoreTerminal, IDisposable, IMarker } from '../../src/common/Types';
 import * as playwright from '@playwright/test';
 import { IBuffer, IBufferCell, IBufferLine, IBufferNamespace, IBufferRange, IDecoration, IDecorationOptions, IModes, IRenderDimensions, ITerminalInitOnlyOptions, ITerminalOptions, Terminal } from '@xterm/xterm';
 

test/playwright/tsconfig.json

@@ -17,14 +17,6 @@
     "noImplicitAny": false,
     "declaration": true,
     "moduleResolution": "nodenext",
-    "paths": {
-      "browser/*": [
-        "../../src/browser/*"
-      ],
-      "common/*": [
-        "../../src/common/*"
-      ]
-    },
     "target": "ESNext",
     "module": "nodenext",
     "composite": true