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just to add a bit more, looking into this, now, if I use this:

```      const route = new aws.apigatewayv2.Route('apiRoute', {
        apiId: apigw.id,
        routeKey: '$default',
        target: pulumi.interpolate`integrations/${integration.id}`,
      })

      const stage = new aws.apigatewayv2.Stage(
        'apiStage',
        {
          apiId: apigw.id,
          name: env,
          routeSettings: [
            {
              routeKey: route.routeKey,
              throttlingBurstLimit: 5000,
              throttlingRateLimit: 10000,
            },
          ],
          autoDeploy: true,
        },
        { dependsOn: [route] },
      )```

and then use name: stage.invokeUrl,

that points to the correct url (but I'd need to hack it and remove https:// and the /stage at the end)

so to even better explain, the route 53 record seem to point to the *API Gateway domain name* but I feel like it should point to *the stage invoke url*