I have been setting up several server side GTMs for my company in the last months. I have deployed both App Engine Flexible versions, as well as Cloud Run hosted ssGTMs.
I found using Cloud Run easier to setup and also cheaper as long as you stay under 300 million requests per month. Custom domain setup is also only slightly different.
The official documentation Basically only covers App Engine and Manual deployment.
I was wondering if there is any downside towards using Cloud Run for hosting your ssGTM besides potential cold starts (which I do not really care about).
I'm not very familiar with GTM but here are few things for using Cloud Run you have to figure out first.