Terraform - setting up Firebase as Identity Source

Hello terraform question here, I recently discovered that to set up Firebase as Identity Source for my HTTP. Gateway I need to use aws_gatewayv2_* resources on terraform.
I don’t understand how to set this properly up now as all tutorials / articles I’ve read seem to be incomplete or not correct (?) because they create an own aws_apigatewayv2_api resource for each endpoint. If I understood correctly then you should have one main aws_apigatewayv2_api resource and then each endpoint should be a aws_apigatewayv2_route and point to a aws_apigatewayv2_api.
I keep getting error creating API Gateway v2 route: BadRequestException: Unexpected or malformed target in route null. Correct format should be integrations/<integration_id>.
But I don’t really understandwhy nor do I see any issue

resource "aws_apigatewayv2_integration" "auth_integration" {
  api_id                 = aws_apigatewayv2_api.loremio_gw_2.id
  description            = "Lambda Serverless Upstream Service"
  passthrough_behavior   = "WHEN_NO_MATCH"
  payload_format_version = "2.0"
  # Upstream
  integration_type     = "AWS_PROXY"
  integration_uri      = aws_lambda_function.loremio_auth_lambda.invoke_arn
  connection_type      = "INTERNET"
  integration_method   = "POST"
  timeout_milliseconds = 29000
  lifecycle {
    ignore_changes = [

# the authorizer 
resource "aws_apigatewayv2_authorizer" "firebase_authorizer" {
  name            = "firebase_authorizer"
  identity_sources = ["$request.header.Authorization"]
  jwt_configuration {
    issuer = "[https://securetoken.google.com/myproject-b3439](https://securetoken.google.com/myproject-b3439)"
    audience = ["myproject-b3439"]
  authorizer_type = "JWT"
  api_id          = aws_apigatewayv2_api.loremio_gw_2.id

# the route
resource "aws_apigatewayv2_route" "auth_route" {
  api_id    = aws_apigatewayv2_api.loremio_gw_2.id
  route_key = "GET /auth"
  target = "integrations/${aws_apigatewayv2_integration.auth_integration.api_id}"
  # Authorization
  authorizer_id = aws_apigatewayv2_authorizer.firebase_authorizer.id

# main api
resource "aws_apigatewayv2_api" "loremio_gw_2" {
  name          = "loremio api gateway v2"
  protocol_type = "HTTP"

I’m pretty sure that api_id is not an output of aws_apigatewayv2_integration.

So this line:

should be changed possibly to this or something else.

Thanks I’ll give it later a try