Tag Manager offers to provision a server for you on Google Cloud. Google itself says that setup is for testing only. It runs in us-central1 in Iowa, whatever country your visitors are in, and it doesn't support a production workload. Fine for learning, not for a shop.
For production there are two routes. You run it yourself on Cloud Run: Google recommends at least two instances, each with 1 vCPU and 0.5 GB of memory, at roughly $45 per instance per month. Or you choose manual provisioning and paste the config string into a hosting service such as Stape or Taggrs.
We compared both routes, costs included, in Cloud Run or Stape.io and Taggrs or Stape.io.