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/benchmark/EscapeSequenceParser.benchmark.ts

@@ -4,12 +4,12 @@
  */
 import { perfContext, before, beforeEach, ThroughputRuntimeCase } from 'xterm-benchmark';
 
-import { EscapeSequenceParser } from 'common/parser/EscapeSequenceParser';
-import { C0, C1 } from 'common/data/EscapeSequences';
-import { IDcsHandler, IOscHandler, IApcHandler, IParams } from 'common/parser/Types';
-import { OscHandler } from 'common/parser/OscParser';
-import { DcsHandler } from 'common/parser/DcsParser';
-import { ApcHandler } from 'common/parser/ApcParser';
+import { EscapeSequenceParser } from '../../src/common/parser/EscapeSequenceParser';
+import { C0, C1 } from '../../src/common/data/EscapeSequences';
+import { IDcsHandler, IOscHandler, IApcHandler, IParams } from '../../src/common/parser/Types';
+import { OscHandler } from '../../src/common/parser/OscParser';
+import { DcsHandler } from '../../src/common/parser/DcsParser';
+import { ApcHandler } from '../../src/common/parser/ApcParser';
 
 const SIZE = 5000000;