I am using a Shopify App to aggregate products into my site. Right now, merchants can install my app and then the app will automatically copy all their products to my site.
After the initial install, I'd like new products to automatically be copied over as well but without the merchant needing to do anything.
I see there is a way to have the merchant manually go in to Settings > Notifications but I'd like it automatically setup when they install the app, nothing more needed.
Is this possible?
I'm not aware of a way to trigger webhooks as you described.
But as a suggestion, when you app is installed you can trigger a background job to fetch all products in the store via GraphQL or Rest API. This way your customer doesn't need to take any extra steps.
That is currently how I have it setup and was going to re-run the job daily or weekly to track new products. Would there be any issue with API rate limiting?
There will be issues with the rate-limiting. You need to handle that using the leaky bucket algorithm.
More details can be found in the below link;
Shopify Leaky Bucket
Also, remember when you are calling anything don't forget to use the Shopify pagination API.
Shopify Pagination API