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/tsconfig.json

@@ -11,12 +11,7 @@
     "moduleResolution": "nodenext",
     "strict": false,
     "target": "es2021",
-    "module": "nodenext",
-    "paths": {
-      "common/*": [ "../../src/common/*" ],
-      "browser/*": [ "../../src/browser/*" ],
-      "Terminal": ["../../src/Terminal"]
-    },
+    "module": "nodenext"
   },
   "include": [
     "./**/*",