Collection update doesn't affect product update date

We get the updated product from the Shopify shop via this endpoint: “get /admin/api/2023-04/products.json?..” with “updated_at_min” filter. This filter works for all product fields, for example if you update the product title now and try to get products.json with “updated_at_min” from 1 minute ago, you will get the updated product.

But if you change the collection of the product, with “updated_at_min” you cannot get the updated product. It seems to me that changing the collection doesn’t affect the update time of the product. For some shop-owners who have thousands of products, we should from time to time check all his product to find collection of which product is already changed. And it make a lot of load on our server.

Does anyone have any solution to get only product thier collection is changed?