Hi, sorry for the delay in replying.
For local trains and buses, you can just show up at the station and ask for help.
For the Shinkansen, it will depend. If the person can walk to their seat, then you could fold the wheelchair and put it near the back of he carriage behind the last row of seats (but note that there is really not enough luggage space on the train and you might have trouble finding a place to put it). If the person cannot walk and needs to stay in the wheelchair, or have it nearby, then you will need to book the wheelchair seats at a “Midori no Madoguchi” (Green Ticket Window) at a train station in advance. The process can take a bit of time, so you may want to book a few days in advance.
I looked up Peach Air and it looks to have gotten much better than the past. Before, the LCC (Low Cost Carriers) like Peach Air often required to to get a doctors letter – which was a bit silly. They don’t seem to list that now and all you need to do is send in a form a few days before your flight. You can find the form and instructions here: https://www.flypeach.com/en/lm/ai/airports/special_support/disabilities
Hope this helps!