I recently received an email requesting I update a custom app because the endpoint will no longer support smart collections.
The Collect resource no longer works with smart collections. Migrate your app to use the new Collection endpoints.
I specifically use that endpoint because it appears to be the only way to actually retrieve products with a value of their manual sort order, via the "sort_value" key. If I need to migrate, where/how to access product manual sort order under the required API version?
This is actually outlined in the doc you linked:
GET /admin/collection/id/products.json: Returns the products for the collection in the collection's sort order. Works for both smart collections and custom collections.
The response from that endpoint returns an array of products, in the collection's sort order.