This is a labelled toy model, not a physics simulation. One honest rule runs everything: light travels at a finite speed (300,000 km every second, real value), so every trip costs time. The drawn messenger is slowed down enormously so you can watch it cross; the toy clock counts "ticks", and each scene says what one tick means there - 1 second at the Moon, 1 minute at the Sun, 1 year at the star.
What is real: light travels in straight lines (sharp shadows); a bounce changes direction, never speed (moonlight is bounced sunshine); moonlight is about 1.3 seconds old when it reaches you; sunshine is about 8 minutes 20 seconds old; the nearest star's light is about 4.3 years old. Looking far away really is looking back in time - NASA's own pages say so, word for word.
Left out on purpose: colors and wavelengths, lenses and eyes working, what light "is made of". The star going dark is a pretend question, not a prediction. No real observations, locations, or personal details are used; nothing about you leaves this page.
Sources: NASA Space Place ("What Is a Light-Year?", "All About the Sun") and NASA's Webb explainer "How Does Webb See Back in Time?". Links are in the project readme.