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>

addons/addon-serialize/benchmark/SerializeAddon.benchmark.ts

@@ -6,8 +6,8 @@
 import { perfContext, before, ThroughputRuntimeCase } from 'xterm-benchmark';
 
 import { spawn } from 'node-pty';
-import { Utf8ToUtf32, stringFromCodePoint } from 'common/input/TextDecoder';
-import { Terminal } from 'browser/public/Terminal';
+import { Utf8ToUtf32, stringFromCodePoint } from '../../../src/common/input/TextDecoder';
+import { Terminal } from '../../../src/browser/public/Terminal';
 import { SerializeAddon } from 'SerializeAddon';
 
 class TestTerminal extends Terminal {

addons/addon-serialize/benchmark/tsconfig.json

@@ -6,24 +6,36 @@
     ],
     "rootDir": "..",
     "outDir": "../out-benchmark",
-    "types": ["../../../node_modules/@types/node"],
+    "types": [
+      "../../../node_modules/@types/node"
+    ],
     "moduleResolution": "nodenext",
     "strict": false,
     "target": "es2021",
     "module": "nodenext",
     "paths": {
-      "common/*": ["../../../src/common/*"],
-      "browser/*": ["../../../src/browser/*"],
-      "SerializeAddon": ["../src/SerializeAddon"],
+      "SerializeAddon": [
+        "../src/SerializeAddon"
+      ],
       "@xterm/addon-serialize": [
         "../typings/addon-serialize.d.ts"
       ]
     }
   },
-  "include": ["../**/*", "../../../typings/xterm.d.ts"],
-  "exclude": ["../../../**/*test.ts", "../../**/*api.ts"],
+  "include": [
+    "../**/*",
+    "../../../typings/xterm.d.ts"
+  ],
+  "exclude": [
+    "../../../**/*test.ts",
+    "../../**/*api.ts"
+  ],
   "references": [
-    { "path": "../../../src/common" },
-    { "path": "../../../src/browser" }
+    {
+      "path": "../../../src/common"
+    },
+    {
+      "path": "../../../src/browser"
+    }
   ]
 }