I searched all over the Internet and found nothing. Projects often have tokens in different networks with the same name and all have the same price. How can this be achieved?
by a allowing users to bridge the token.
Let's say we have a token on two chains. On chain A the token price is 100$ and on chain B it's 150$. Now if there is a way to bridge tokens from A to B and back then you can buy 1 token on chain A for 100$, then bridge it over to B and sell it there for 150$.
If you list your token on any exchange and you can deposit both versions of the token on the exchange then the price will also be the same as the exchange would be a bridge + another market where the token is traded.