Perhaps you should try to understand what problem any products/features solves before implementing them.
By default, Google’s tracking codes (AdSense, Analytics, etc) are served from Google’s domains and the tracking cookies are 3rd-party cookies. But these days, there are a lot of ad-blockers and privacy tools that block 3rd-party cookies or even block domains used for analytics and ads at the DNS level.
That’s great for privacy, but I’m sure you know what problem this creates for website owners and advertisers.
The purpose of Google Tag Gateway is to serve that same Google tracking code from your own domain, rather than Google’s domain… making this first-party tracking.
You can use Google Tag Gateway together with Google Site Kit without issues: just make sure to uncheck “Setup tag” in your Cloudflare dashboard if you’re using Site Kit to inject the tag already.