The link lists a number of conditions - flying with ANA in one of the listed classes, etc. If you don't meet the criteria, there are a couple of "sky lounges" - bare bones, but reasonably priced if you just want soft drinks and a place to sit / work for a few hours. There are also paid showers.
https://tokyo-haneda.com/en/service/...es/lounge.html

If you don't want to enter Japan, you can transit without passing through immigration or customs. Just follow signs for transit / international connections. If you don't have your boarding pass, stop at the transit counters.

If you are interested in getting out of the terminal but you don't want to go into central Tokyo, there are a few places near the airport that are okay for killing time. Shops and restaurants in Kamata, or the onsen at Heiwajima, for example. To do anything outside of the terminal, you will need to go through immigration and customs, and come back through security and immigration:
https://matcha-jp.com/en/10065
https://www.heiwajima-onsen.jp/en/