You seem to have got caught in the first "trap"
when you chose a JR website.
Your first leg Ueno -- Nagano -- Matsumoto
is fully inside the JR-EAST network.
Your seats in Shinkansen Kagayaki and Limited Express Shinano trains
can be reserved through JR-EAST Train Reservation website.
- JR-EAST Train Reservation https://www.eki-net.com/pc/jreast-shinkansen-reservation/English/wb/co...
Please make sure
that you can pick up your tickets booked through this website by 21:00 (9 p.m.)
of the day before your rides,
at a JR-EAST ticket window in Tokyo.
(Some ticket windows get closed before 21:00.) https://www.jreast.co.jp/e/ticketwindow/trainreservation.html
To use this reservation website,
you first register your membership
with your credit card of a designated brand. https://www.eki-net.com/top/train_reservation/english/faq/faq.html#q10...
JR seat reservation is doable
from the day one month before the train departs from its first station.
While the Hokuriku Shinkansen is composed of
the JR-EAST part (Tokyo -- Nagano -- Joetsumyoko)
and the JR-WEST part (Joetsumyoko -- Kanazawa),
the reservation websites of both JR-EAST and JR-WEST
cover any section regardless of their operation boundary.
the recently-launched JR-WEST reservation website
seems not designed for passengers traveling with any JR pass.