I live in Tokyo. The situation in Tokyo is not worse than so many other places, but I still doubt June will be a great time to go. The current state of emergency runs until May 31st. I don't believe it will be extended, but let's see. But it certainly does not mean that the city will be back to normal just at once. Also, the entry restrictions for non Japanese citizens are not tied to the state of emergency declaration, and it is quite a separate topic of when that will be relaxed. I would not count on June if it was me.