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>

bin/test_unit.js

@@ -8,10 +8,6 @@ const path = require('path');
 
 const COVERAGE_LINES_THRESHOLD = 40;
 
-// Add `out` to the NODE_PATH so absolute paths can be resolved.
-const env = { ...process.env };
-env.NODE_PATH = path.resolve(__dirname, '../out-esbuild');
-
 let testFiles = ['**/out-esbuild/**/*.test.js'];
 
 let flagArgs = [];
@@ -46,7 +42,7 @@ if (checkCoverage) {
     args,
     {
       cwd: path.resolve(__dirname, '..'),
-      env,
+      env: process.env,
       shell: true,
       stdio: 'inherit'
     }
@@ -59,7 +55,7 @@ const run = cp.spawnSync(
   [...testFiles, ...flagArgs],
   {
     cwd: path.resolve(__dirname, '..'),
-    env,
+    env: process.env,
     shell: true,
     stdio: 'inherit'
   }