Connecting Flight with ANA

I'm flying from Toyama Airport to Hakodate Airport.
There is a stopover at New Chitose Airport.
I've never had a stopover before.

When I exit my flight at New Chitose Airport,
Do I have to pick up my luggage, checkin to the next flight, and drop my luggage off all over again?
Or do they move my luggage for me?

If all your reservations are done with ANA, then it should be simple for ANA to check your luggage all the way to HKD. At CTS you may be met by an ANA staff that may guide you to your corresponding gate to minimize the time spent. I am not too sure it happens all the time, but I have heard of this occurring at some airports.

When you check in your luggage at Toyama airport, the ground stuff will ask you "Do you have a connecting flight?" If she/he does not ask, you can say "I have a connecting flight to Hakodade". Then they will ask you to show them the ticket. Or if you just show your passport, they might understand your flight schedule. You can ask them "Will my luggage go through to Hakodate?" and they will answer "Sure, pick up your luggage at Hakodate."

I am not sure about the transit process in Chitose, but you will have plenty of time (2+ hours) as far as I searched the flight schedule so you might better go out of the security zone where you can find many restaurants to have lunch. After that the process is the same as that in Toyama though you don't need to check in your luggage. There are some ground staff with their uniform so you can easily find them and ask them how to do.

I would advice you to contact the staff at the gate at Chitose, tell them you have a connecting flight and ask them how to proceed from there.

I did the same last December when I had a connecting flights at Chitose: When we got off the plane we reached out to the staff waiting at the end of the gate and they checked our names and we were shown into the waiting area where we found our new gate for departure. The staff had a list of passengers. Our luggage made it to the final destination without us taking care of this.