Lost Australian Passport in (Tokyo?)

Hi all, I require assistance with the next steps forward after I’ve lost my passport in Tokyo. I can see all the necessary information online but there is alot, and I just want to confirm a few things.

15 Days in Japan, Tokyo for 5 days, Kyoto for 3 days, Osaka for 4 days, and back to Tokyo for last 3 days.

I have just arrived to Kyoto for the first day and upon arrival to the hotel I realised I don’t have my passport with me. I have checked in fine and have notified reception. They have contacted my last hotel and will give me an update soon.

If I have lost it, my understanding is I will need to contact the Australian embassy to reissue an emergency replacement before I return home. I wanted to ask: I can see there is one in Tokyo and Osaka, will I need to use up a day in Kyoto to visit one of these? Should I contact the nearest police station to the hotel I was staying in Tokyo? I would appreciate any assistance in this because it’s my first time in Japan and I’m quite stressed. Thank you.