Japan in September

Been thinking about visiting Japan in September, but not sure what to expect.

I wanted to experience the alp mountains which are apparently not accessable in October or November, august is a bit too warm and crowded as I have experienced before.

Due to work I cannot visit Japan in October.

Should I expect typhoons disrupting travel plans several days a week? Should I be planning for backup accommodation in case of cancellated flights or trains?

I have been to Japan in October twice and had to reschedule my plans due to typhoon once as far as I can remember.

Some people go overboard when describing hurricanes in Japan. September has some typhoons but they are not blowing through every other day at all. When they do come, they usually move past in a day or two. In severe cases, transportation can be disrupted for the day. But many times they are not that bad, and life goes on as usual. I've ridden my motorcycle down the streets when there was a typhoon once - aside from some gusty winds, it was no big deal. The storms are not all the same.
That said, yes, you should look at the weather forecasts while in Japan, and try to keep a flexible schedule.

No issues travelling in September. The minimal Typhoons are generally weaker. And weaker again going further north.

Should I be planning for backup accommodation in case of cancellated flights or trains?

I wonder what you exactly mean. For example, I find that it has become so common for international flights to be delayed or canceled anywhere in the world at any time, and if so, the airline would arrange accommodation. And in the 55 years of living in Japan, there was one time I couldn't go home because the Shinkansen couldn't go through the harsh rain, and a lot of people just spent the night at the train station floor. (I was able to book the crummy hotel in the suburbs that no one else knew of.)

So, one can manage. Meanwhile, although I'm no expert, I find that weather in the mountains are unpredictable at all times. You just have to pay attention to notices for climbers. The website below advises that September may be cold but okay if it's a day trip.
https://www.yamakei-online.com/yama-ya/detail.php?id=2103

On a related note, September is my favorite month for visiting calm beaches and islands. I can often have the whole beach or two for myself. But there would be no lifeguards on duty, so I need to watch out for myself and stay where my feet could touch the bottom of the water.

I wanted to experience the alp mountains which are apparently not accessable in October or November

Early to mid October should still be fine for hiking, and some mountain huts are open till early November.

https://thejapanalps.com/en/cottage-hotel/cottage-camping/