I'm not an expert in ad affairs. With this information on the table, consider the following:

I subscribe to a "price alert" for a product in my sellers app. The price gets triggered, and because there's a lot of demand for this item, I have to be fast.

This, for me, would justify the "push notification".

But, would this also be considered an "ad"? From the definition of the word "advertisement"[1], which says it's "a notice, picture or film telling people about a product, job or service", it would qualify as an ad.

[1]: https://www.oxfordlearnersdictionaries.com/definition/englis...