Sony recently said the PS5 doesn't have a web browser. That's not entirely true. There is a web browser...but you can't access it whenever you want.
Unlike the PS4, the PS5 doesn't have a web browser app built into the system's UI. Gamers can't start up a web app and surf the internet like they can on the PS4. The reasons for this are two-fold: Sony doesn't really think people need a web browser, but more importantly, it reduces the opportunities for hacks and exploits. The PS4's web browser led to a kernel access exploit on v1.76. Sony doesn't want to repeat the same mistake.
On the other hand, the PS5 does technically have a web browser, but it's only available when you first set up the console. The browser is restricted though and you can't actually change the URL. The browser comes up when you click on the ratings and health and safety sections on console setup.
When setting up my PS5, I clicked on all the options and was met with various web pop-ups that directly connected to Sony's and the ESRB's websites. The console didn't let me take screenshots so I had to take a snap with my phone. After startup, I wasn't able to access the web pop-up portions again.
Also, when I linked my Twitter account to the PS5, I got an email from Twitter saying I just signed in on a new Safari browser. So the PS5 runs on a webkit version of Safari just like the PS4.
Oddly enough the PS5's UI does have a section for the web browser. There's settings to tweak and adjust, like clearing cookies and website data.
Sony exec Hideaki Nishino recently said the PS5 could get a public and accessible web browser at some point:
"Currently, we do not intend to install a web browser on PS5," Sony VP Hideaki Nishino said in a recent interview with AV Watch.
"Of course, I use it as a component to use various network functions, but I have doubts about whether a web browser is required for game consoles as an application, so please let me know."