JR Central, JR West and JR Kyushu have introduced a rule for oversized baggage carrying inside their Shinkansen trains on 20 May 2020.
This new rule is not recognized by foreign tourists due to COVID-19 crisis which reduced the traffic of foreigner drastically. However this new rule will continue even COVID-19 is expelled.
The new rule is for passengers carrying baggage with total dimensions over of more than 160 cm. The new rule is called "baggage 160" and if you are carrying a baggage above size, you have to reserve a seat with oversized baggage area. There are 5 seats allocated for these passengers and located in the most rear row of the reserved car.
Which means if you are traveling with Japan Rail Pass and carrying an oversized baggage, you have to make a seat reservation all the time on Tokaido, Sanyo and Kyushu Shinkansen. Oversized baggage is not allowed to bring inside non-reserved cars. Then, there is no extra supplement for oversized baggage area.
Actually there is a rule for carrying baggage on Shinkansen trains. The baggage should not exceed total dimensions of 250 cm, up to 30 kg and you can bring up to two pieces of baggage and your personal items such as umbrella, handbag and etc. Which means you can not bring two middle size suitcases and a carryon on Shinkansen trains.
Anyway, no worries. Usually airlines allow checked baggage not exceeding total dimensions of 158 cm. If you did not have any problem during check in at airport or you did not have to pay a fee at airport, there is no need to care "baggage 160". For your info, Essential Lite Check-in L 91L from Rimowa is 78+51+26.5= 155.5cm.