When using Meta Conversions API Gateway, you do not need a GTM server-side container.
However, you need to create Meta’s CAPIG on Stape.
Meta Conversions API Gateway works based on the data that FB pixel sends. It means that every time when CAPIG sees event triggered by FB pixel, it sends server events.

Meta Conversions API Gateway tracks server events using data that Meta pixel receives. Each event that Meta pixel tracks will be automatically tracked using Meta Conversions API Gateway. You can manage what events you want to send using CAPI Gateway via the hub. Just turn the on or off toggle in from of each event. 

If you want to track any new event using Conversions API Gateway, then you should set up web tracking for this event. Then, after Meta pixel detects the event, it would be automatically added to Conversion's API Gateway.