Shopify will maintain a few paths to to extend POS including POS UI Extensions (recommended) and the ability to embed apps in POS. When you say “app website tiles for POS”, I believe you mean apps embedded in POS, which will remain an option (i.e., we are not deprecating the ability to maintain apps embedded in POS).
POS Links can be rebuilt as POS UI Extensions or these apps can be embedded in POS.