The story concept
After one bite, our hero shoots light from his eyes and spots breakfast blocks away. The glowing eyes and citywide vision are invented for the joke.
What the sources actually say
Carrots contain beta-carotene, which the body can convert to vitamin A. Vitamin A helps maintain normal vision, including vision in low light. The US National Eye Institute explicitly treats the idea that eating lots of carrots gives good vision as a myth: people generally get the vitamin A they need from a balanced diet.
Where the evidence stops
Too little vitamin A can impair vision, particularly in low light. That does not mean extra carrots improve the eyesight of someone who already gets enough. The animation is not a test of a real person or a promise of a measurable vision change.
The useful takeaway
Eat a varied diet that includes sources of vitamin A. If your vision changes or you struggle to see in low light, get advice from an eye care professional instead of trying to fix it with extra carrots.