Hasan Savran shows how you can create a trigger in Cosmos DB:
You have options if you need to use any type of triggers in Cosmos DB. There are two types of triggers in Cosmos DB. First one which I will cover here is the regular triggers which can be executed before (Pre-Triggers) or after (Post-Triggers) an operation. This type of triggers is written in JavaScript and you need to register them to a collection just like stored procedures. Second type of triggers can be created by Azure Functions and you can find more information about them in my older posts.
Pre-Triggers and Post-Triggers do not take any input parameters. Since Cosmos DB needs to work more work to execute triggers, you will end up with higher Request Units for your queries. They might name triggers, but both do not get executed automatically with every operation. You need to call them programmatically if you want to run them. If trigger throws any error for any reason, transaction will roll back and data will not be saved to the database.
Naturally, triggers are going to have a performance impact on your system regardless of the choice of data platform.