Why should we treat a minor wiki page and some dude's personal site (who disagree with each other on totals) as authoritative proof Ikea is wrong about it's own catalog? Especially when it's not hard to find 1st/3rd party sources claiming an order of magnitude more products. Keep in mind, some things will also fall off the catalog over time.
I’m going to guess that a good chunk of products are named but never released. I’d love to know what products IKEA develops but decides to not release.
It's more likely that the whole product catalog contains 2-3k products. [1][2][3] So no, you don't.
[1] https://www.ikea.com/us/en/cat/products-products [2] https://lar5.com/ikea (~ 2200) [3] https://namingschemes.com/Ikea_Product_Names (~ 1300)