Hi julund. @kenneth_rogers posted some good information. I certainly don't consider myself an expert in Quizzes.Next, but have been playing around with it for a while and did a bit of testing in my sandbox.
This is what I would suggest you try to see how it works.
1- Add all your existing questions from a bank to a quiz in Quizzes Classic, like you did.
2- From the Settings tab, export the quiz as a QTI file.
3- Go in to Quizzes.Next and in the upper right-hand corner click on the three dots and "Manage Item Banks".

4- Create a bank named as you like.
5- Click in to the empty bank.
6- Click on the three dots in the upper right-hand corner and "Import Content"

7- Select the QTI file you exported previously.
8- Hopefully it worked!
9- Repeat for your other question banks from Quizzes Classic
It is basically what the document linked above describes but should create an item bank instead of importing the questions into a Quizzes.Next assessment.
I hope this helps, but please let us know if you run into issues!
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