What are the tickets for?

Solution 1:

The silver tickets can be used to make bets. Somewhere around day 10, your email client gains the bet button, which allows you to wager silver tokens to attempt to reach a certain combo with a randomly determined active menu.

Screenshot of betting interface

Golden tickets become useful once you reach a 4-star rating. Spoiler below:

Once you reach that rating, you'll be contacted by the secret clan of the Temple of Delicious. This will unlock the Hungry Festivities as the third Extra Event. Golden tickets are used to unlock challenges in the Hungry Festivities. Screenshot of third Extra EventScreenshot of third Extra Event