fix(coding-agent): remove process-cwd tool singletons and use tool-name allowlists

- switch SDK/CLI tool selection to name-based allowlists
- apply allowlists across built-in, extension, and SDK tools
- remove ambient process.cwd defaults from core tooling and resource helpers
- update tests, examples, and TUI callers for explicit cwd plumbing
- add regression coverage for extension tool filtering

closes #3452
closes #2835

packages/coding-agent/src/core/footer-data-provider.ts

@@ -101,7 +101,7 @@ export class FooterDataProvider {
 	private refreshPending = false;
 	private disposed = false;
 
-	constructor(cwd: string = process.cwd()) {
+	constructor(cwd: string) {
 		this.cwd = cwd;
 		this.gitPaths = findGitPaths(cwd);
 		this.setupGitWatcher();