Indreams shows PS4 as online, even after powering down
After you turn off the PS4, it will still say connected and show prompts to 'play now'. You can browse dreams, you can click on creation pages, click on Dreams header, browse side-bar and it will not update the PS4 connection status.
The only way to trigger it to realize that the PS4 isn't actually online anymore is by manually refreshing the web page.
I'm not sure if this is just on my end, or if this is how it works for everyone. But when you change pages, shouldn't it check to see if PS4 still connected and catch the error?