To summarize/state things differently:

If you want to stay in the airport (aka 'airside'), you can do that without any visa arrangements. You can eat and drink basically all you can in the F lounge. Technically you can also sleep and shower there, but that's not recommended (there was a recent thread on this); instead book the airport hotel. The airport hotel is airside and is located near the gates and lounges.

You can also get an entry visa - either (a) in advance, through an organizer (such as Marhaba Services or the hotel you are staying at), or (b) try your luck applying for a visa at the airport, with F lounge + airport hotel as a fallback option so your vacation wouldn't be ruined.

The 96-hour transit visa for the UAE is not a UK/Schengen style 'Airport transit visa', it is really a stopover visa.