Haneda airport timings

My wife and I land at Haneda on a Wednesday in October 2024 at 22:35. I have booked the Hotel Sunroute plaza in Shinjuku for that night. Late check in there is OK.
My questions are:
How long does it take to get off the plane, go through immigration control, buy train tickets and anything else that is required before we head to the Tokyo Monorail, to Hamamatsucho Station and then to Shinjuku station. We don't want to miss the last train.
OR
Is it recommended to stay for one night at a nearby Airport hotel? Hotel suggestions please.

Thanks for any reply.

Landing in 22:35 pm :So stay that night in hotel located in haneda Airport.

Next day: haneda airport to shinjuku station
You need 1800 yen,so you will go haneda to shinjuku by limousine bus and travel unlimite d ride in toei subway nd tokyo metro subway

Google maps tells you when the last train connection is and yes, it�fs tight. It MAY work out but it as well may NOT. So either you cough up the money for a taxi or get a hotel at the airport