When the PS3 was at its peak, Sony and Google maintained a dedicated YouTube application tailored for the console’s "XrossMediaBar" (XMB) interface. However, as technology advanced, Google shifted the backend infrastructure of YouTube. They moved from older API protocols to newer, more secure data transmission methods (such as the infeasibility of older Flash-based streaming and the adoption of modern DASH protocols).
You can download and install the YouTube app on your Go to product viewer dialog for this item. Ps3 Youtube Pkg Download
Installing a "PS3 YouTube PKG" can restore YouTube functionality on older PS3 systems, but it comes with security, stability, and policy risks when using unofficial packages. For most users, safer options are official updates, using the PS3 browser, or streaming from another device or a modern streaming box. If you choose to use an unofficial PKG, proceed with caution, verify sources, and back up your system first. When the PS3 was at its peak, Sony
Here is an interesting guide on how to approach this, covering the best options and the installation process. You can download and install the YouTube app