Break up LoginComponent into client-specific services.

libs/auth/src/angular/login/extension-login.service.ts

@@ -0,0 +1,25 @@
+import { Injectable } from "@angular/core";
+import { Router } from "@angular/router";
+
+import { LoginEmailServiceAbstraction } from "@bitwarden/auth/common";
+
+/**
+ * Functionality for the extension login component.
+ */
+@Injectable({
+  providedIn: "root",
+})
+export class ExtensionLoginService {
+  constructor(
+    private router: Router,
+    private loginEmailService: LoginEmailServiceAbstraction,
+  ) {}
+
+  /**
+   * Handles the successful login - clears the login email service values and navigates to the vault.
+   */
+  async handleSuccessfulLogin(): Promise<void> {
+    this.loginEmailService.clearValues();
+    await this.router.navigate(["/tabs/vault"]);
+  }
+}