If this were my computer, I’d start on the old machine and install Scrivener 3. I test it with the upgrade guide to get a sense of how Scrivener 3 might handle my projects.
Then, I’d probably upgrade my existing projects to Scrivener 3 on the old computer first.
Once I was sure they were working correctly and my links worked well on the old computer, I’d migrate materials to the new computer and test again. Then, I could work on repairing any broken links if needed.
This Knowledge Base article offers tips on installing to additional computers.
Trying to do the upgrade steps at the same time as migrating to the new computer would be too much for me to manage at once.
And, I’d keep that old computer around until I felt certain the new machine was working well.