Authentication sample is using the old Input System resulting in error spam in the new Unity verisons

How to reproduce:
1. Create a new project
2. Go to Window -> Package Management -> Package Manager -> Authentication -> Samples
3. Import the "UI Example" sample
4. Open the "AnonymousLoginUIExample" scene and enter the Play Mode
5. Observe the results

Expected results: No errors are thrown
Actual results: Errors are spammed because the scene uses the old Input System

Reproducible with: 3.6.1 (6000.0.76f1, 6000.3.15f1, 6000.4.8f1, 6000.5.0b9, 6000.6.0a7)

Reproducible on: macOS Tahoe 26 (M1)
Not reproducible on: No other environment tested

First lines of error:
InvalidOperationException: You are trying to read Input using the UnityEngine.Input class, but you have switched active Input handling to Input System package in Player Settings.
UnityEngine.Input.get_mousePosition () <0xebe02cd40 + 0x0004b> in <3b84fb292fe944019318855b7068acd2>:0
UnityEngine.EventSystems.BaseInput.get_mousePosition () (at ./Library/PackageCache/com.unity.ugui@e2d53fe04c15/Runtime/UGUI/EventSystem/InputModules/BaseInput.cs:95)