In case someone else runs into a similar issue, this might help. It turns out that when I change the configuration slightly, it seems to work fine:

resource "google_cloudbuild_trigger" "test_cloudbuild_trigger" {
  project  = "<project_id>"
  name     = "test-build"
  filename = "cloudbuild.yaml"
  location = "europe-west4"

  github {
    owner = "<org>"
    name = "<repo>"
    push {
      tag = ".*"
    }
  }
}