According to Sony the PS5 does NOT have a "dedicated web browser app" but this is a lie. There is a 'modal' web browser, just like on PS3/PS Vita/PS4 that can be called from an app to load a webpage. It is used on PS5 to load the Users Guide, to login to Twitter/YouTube/Twitch, etc.
HTTPS in modal web browser
There is a bug in the Modal Browser that allows user to bypass HTTPS. See Bugs & Vulnerabilities.